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	Dividing a region in half		2018-02-24
		mandy pose la question : There is a line through the origin that divides the region bounded by the parabola y=4x−5x2y=4x−5x2 and the x-axis into two regions with equal area. What is the slope of that line? Penny Nom lui répond.
	Integrate (x^2 - 4x + 4) ^4/3		2016-09-15
		Ifah pose la question : Hi i have questions please answer Integral 2 sampai 3 dari (x² - 4x + 4) ^4/3 dx Penny Nom lui répond.
	The integral of a sum		2016-03-10
		Rahul pose la question : How to solve definite integral of a sum. The specific problem is as follows, Integral of ( 1+ sum of x^k, k=1 to k=n), x=0 to x=b *dx. The answer is b + sum of b^(k)/k, k=2, to k=n+1. I understand only the integral of first term. But integral of the sum I do not understand at all. Penny Nom lui répond.
	Integration of dx/(x^2+1)^3		2016-01-07
		Ishank pose la question : Integration of dx/(x^2+1)^3 Penny Nom lui répond.
	The area bounded by the X-axis and y=x^(2)-4 from -5 to 0		2014-04-15
		Lexie pose la question : Determine the area that is bounded by the following curve and the x-axis on the interval below. (Round your answer to three decimal places) y=x^(2)-4, -5 ≤ x ≤ 0 The answer is 32.333 but I have no idea how to get there. Penny Nom lui répond.
	Integration from 0 to 2pi of 1/(3cos x + 2) dx		2013-02-04
		ankit pose la question : Integration from 0 to 2pi of 1/(3cos x + 2) dx Harley Weston lui répond.
	An integral		2012-12-16
		Slavena pose la question : integration of (lnx)^2 / x dx Penny Nom lui répond.
	Integral 1/(25-x^2)^3/2		2012-02-22
		John pose la question : Integral 1/(25-x^2)^3/2 Harley Weston lui répond.
	A volume of revolution		2012-01-11
		john pose la question : find volume of solid generated by revolving the region in the first quadrant bounded by the curve y squared=x cubed, the line x=4 and the x-axis about the line y=8. The answer in the back of the book is 704 pi divided by5 Penny Nom lui répond.
	An antiderivative of the square root of (8t + 3)		2011-04-19
		Caitlyn pose la question : I know how to take an antiderivative. But this one's stumping me. I need it to finish a problem. What's the antiderivative of the square root of (8t + 3) ~Caitlyn= Penny Nom lui répond.
	Integrating ln^3x/x		2011-01-14
		ken pose la question : y=ln^3x/x from x=1 to x=11 Penny Nom lui répond.
	The integral of (x^2*exp(x)/(exp(x)-1)^2		2010-08-09
		sujoy pose la question : please find this integral for me int(x^2*exp(x)/(exp(x)-1)^2 Robert Dawson lui répond.
	Integration of sin^3 (2x)		2010-05-29
		ascher pose la question : how do you integrate this equation ∫ sin^3 (2x) dx Robert Dawson and Penny Nom lui répond.
	Integrate the ((4th root of x^3)+1) dx		2010-04-12
		Bridget pose la question : integrate the ((4th root of x^3)+1) dx Tyler Wood lui répond.
	The integral of X^3/the square root of 1-x^2 dx		2010-03-07
		William pose la question : The integral of X^3/the square root of 1-x^2 dx. Harley Weston lui répond.
	Integration of cos (x^2+y^2) dx dy		2010-02-12
		anna pose la question : How do you evaluate the integration of integration of cos (x^2+y^2) dx dy? Tyler Wood lui répond.
	An integral		2010-01-29
		amr pose la question : find the value of the following integral:- (1+x)power (-1/2) dx Robert Dawson lui répond.
	The integral of sqrt(x) * ln(x)		2009-10-12
		Oana pose la question : Hi! Can you tell me please how much is : ∫ (√x * ln x) ? Penny Nom lui répond.
	Integration of cos (x^2) dx		2009-10-12
		Venkat pose la question : How do you evaluate the integration of cos (x^2) dx ? Harley Weston lui répond.
	solve integral of ( x^2+x+1)^5		2009-09-18
		jaka pose la question : solve integral of ( x^2+x+1)^5 Robert Dawson lui répond.
	An antiderivative problem		2009-08-13
		Indrajit pose la question : ∫4e^x + 6e^-x/(9e^x + 4e^-x)dx = Ax + Bloge(9e2x - 4) + C then A=?......B=?.....C=? plz solve it...."^" stands for "to the power of".... Harley Weston lui répond.
	The integral of x^x		2009-06-18
		ANGIKAR pose la question : what would be the integration of (X^Xdx)? give answer in details. Robert Dawson and Harley Weston lui répond.
	The integral of a to power x squared		2009-04-28
		JIM pose la question : WHEN I ATTENDED U.OF T. (TORONTO ) MANY YEARS AGO WE WERE TOLD THE FOLLOWING INTEGRAL COULD NOT BE SOLVED : a to power x squared . is this still true ? CURIOUS , JIM Robert Dawson lui répond.
	The integral of the square root of the sine function		2009-04-07
		Indrajit pose la question : how to integrate this derivative??? ∫√sinx Harley Weston lui répond.
	The area between the x-axis and a curve		2009-02-18
		Lauren pose la question : This is from a homework question I can't figure out. Let R be the region in the fourth quadrant enclosed by the x-axis and the curve y= x^2 - 2kx, where k > 0. If the area of the region R is 36 then what is the value of k? Robert Dawson lui répond.
	The integral of f(x)dx and the integral of f(x-4)dx		2009-01-02
		Katie pose la question : Calculus: If the definite integral from -2 to 6 of f(x)dx=10 and the definite integral from 2 to 6 of f(x)dx=3, then the definite integral from 2 to 6 of f(x-4)dx= ? I don't understand how to solve definite integrals when the function has something more than just x inside the parenthesis such as f(4-x). Robert Dawson lui répond.
	Antiderivative of 1/(x(1 - x))		2008-10-22
		Matt pose la question : derivative of dx/(x(1-x)) From what I've seen I should break apart the equation as such derivative of dx/x - dx/(1-x) and then get the 2 corresponding log functions. If that is correct why does this factoring work, if that is incorrect what is the proper way to find the derivative. Harley Weston lui répond.
	Integration		2008-10-17
		hazela pose la question : integration of x sinx cosnx Harley Weston lui répond.
	Integral of X^2		2008-07-28
		Hemanshu pose la question : Integral of X^2 Janice Cotcher lui répond.
	The volume of a solid		2008-06-04
		Tom pose la question : The base of a certain solid is a circle of radius 2 while cross sections perpendicular to the base are isosceles triangles of height 1. What is the volume of the solid? Harley Weston lui répond.
	The weight of a concrete column		2008-05-11
		russell pose la question : a cylindrical form is filled with a slow curing concrete. The base of the form is 10 ft in radius, and height is 25 ft. while the concrete hardens, gravity causes the density to vary from a density of 90 lbs/ft^3 at the bottom to a density of 50 lb/ft^3 at the top. Assume that the density varies linearly from the top to the bottom, and compute the total weight of the resulting concrete column Harley Weston lui répond.
	Integrate 2x(x^2-1)^5 dx		2008-04-17
		joey pose la question : pls help me to integrate 2x(x^2-1)^5 dx using the substitution u=x^2-1 Harley Weston lui répond.
	The integral of dx / (4x^2 - 25)^3/2		2008-04-01
		Meghan pose la question : I have a question from the trigonometric substitution of my calculus course. integral of dx / (4x^2 - 25)^3/2 Harley Weston lui répond.
	Integrate (4+x^2) / (x (2+x)^2)		2008-02-25
		Russell pose la question : integrate (4+x^2) / (x (2+x)^2) I really need to know the steps involved in doing this integral, I already have the answer through wolfram integrator but for some reason can not get to the answer given. Please help Harley Weston lui répond.
	Two regions with equal area		2008-02-13
		James pose la question : There is a line through the origin that divides the region bounded by the parabola y=3x-5x^2 and the x-axis into two regions with equal area. What is the slope of that line? Harley Weston lui répond.
	Integration by parts		2008-01-30
		seth pose la question : hi i really dont understand integr ation by parts. for example, the integral(t^2sintdt. i have u=t^2 and v'=sint also u'=t^/3 v=-cost for the formula i have uv-integralvu' dx this is all well and good but i cant get it right. Harley Weston lui répond.
	The integral of Sqrt(sin x)		2008-01-24
		tariq pose la question : find integration Sqrt(sinx) dx , from x=bi/4 to 3bi/4 Harley Weston lui répond.
	An integral		2008-01-24
		Meghan pose la question : Evaluate the indefinite integral of (x^3 +1)^(1/3) * x^5 * dx. Brennan Yaremko lui répond.
	Integration		2008-01-23
		Russell pose la question : how to integrate 1/x ln^2 [x] dx Harley Weston lui répond.
	Two integrals		2007-11-09
		Akilan pose la question : how to integrate these (tan x)^6(sec x)^4 and sinh(x)(cosh(x))^2. Please send me how to do this question. Having exams on Monday. Please help. Harley Weston lui répond.
	Integration		2007-02-02
		Jenna pose la question : How do I integrate ( ln(x) ) / ( x^2 ) ? Penny Nom and Claude Tardif lui répond.
	The volume of a frustum of a pyramid		2007-01-17
		Sam pose la question : Find the volume of a frustum of a pyramid with square base of side b, square top of side a, and height h. Penny Nom lui répond.
	Integrate x^8 (x^8 + 2)^2 ((x^8 + 2)^3 + 1)^4		2007-01-09
		James pose la question : How do you integrate x^8 (x^8 + 2)^2 ((x^8 + 2)^3 + 1)^4 Penny Nom lui répond.
	An Integral		2006-07-30
		Aniket pose la question : I am Aniket studing in 12 th standard At Mumbai I have following integration problem please give me a solution integral of 1/under root of (5x2 - 2x) dx Penny Nom lui répond.
	The integral of tan^4x		2005-03-31
		Nicole pose la question : college student. need help with tough integral. the integral of 2tan4xdx Penny Nom lui répond.
	Approximating an integral		2005-01-27
		A student pose la question : i used excel to find the area under a graph instead of integrating the function the analytical way. These are the different answers i got with different width of the x-values, the smaller the x-increment gets the more precise the area is when compared to the answer obtained the numerical way. I have trouble seeing why the answers i get is getting bigger and bigger and not smaller can someone plz explain? Penny Nom lui répond.
	Integrating e^sin(x)		2004-08-04
		A student pose la question : I need to know that how to solve the integral " e^sin x", Harley Weston lui répond.
	A helicopter rises vertically		2003-09-02
		Kate pose la question : A helicopter rises vertically and t seconds after leaving hte ground its velocity is given in feet per second by v(t) = 8t + 40 / (t+2)2 How far above the ground will the helicopter be after 3 seconds? Penny Nom lui répond.
	Odd powers of sine and cosine		2003-06-25
		Antonio pose la question : Can you please tell me how to integrate a trig function involving sine and cosine? I know if the powers of both the sine and cosine are even and nonnegative, then I can make repeated use of the power-reducing formulas. But for the question I have on my hand, the powers of both sine and cosine are odd: ( sin3x + cos7x ) dx. Harley Weston lui répond.
	Integrating e^x sin(x)		2003-05-03
		Lech pose la question : I am having trouble integrating the following expression by parts: ex sin(x) I used the integrator at http://www.integrals.com/ to find the solution, ? 1/2 ex cos(x) + 1/2 ex sin(x). This is easy to confirm by differentiation, however I am confounded as how to arrive at the answer. Penny Nom and Claude Tardif lui répond.
	Integration of 1/(2+cos(x))		2003-01-07
		A student pose la question : integral from pi to 0 of dx/(2+cos x) i used the substitution t=tan(x/2) and i ended up with integral from +infinity to 0 of 2dt/(t2+3) which looks like an inverse tan function , and i ended up with sqr(27)/2 pi , which is not the same as my calculator's answer , so i suspct i am doing some thing wrong. can some one tell me where i am going wrong please. Penny Nom lui répond.
	Integrating x^x		2002-06-18
		Jeremy pose la question : I am a student at the University of Kansas and I am wondering if there is a general anti-derivative for x x (i.e. the integral of x x dx)? I've looked in a bunch of Table of Integrals and have found nothing (can you guys find it?), so I'm sort of wondering if this may be a research type question. Claude Tardif lui répond.
	Arc length		2002-04-17
		Vix pose la question : Find the point on the curve r(t)=(12sint)i-(12cost)j+5tk at a distance 13pi units along the curve from the point (0,-12,0) when t=0 in the direction opposite to the direction of increasing arc length. Harley Weston lui répond.
	The probability that the area of a triangle is smaller that 1/8		2001-12-21
		Hoda pose la question : Given unit square pick two points on adjacent sides of the square , what is the probability that the area of the resulting triangle is smaller that 1/8? I tried to tackle the problem by first sketching a square with the four vertices at (0,0), (1,1), (0,1) and (1,1). The answer seems to be the area under the curve y=0.25/x between 1 and 0, but how can you integrate such a function when ln0 is undefined? any help would be highly appreciated. Andrei Volodin lui répond.
	Area between curves		2001-06-13
		Phil pose la question : question 1 find the area bound by the curves y = x2 + 2x + 3 and y = 2x + 4 question 2 Find the volume generated by rotating the curve x2 + y2 = 9 about the x-axis Harley Weston lui répond.
	National consumption function		2001-05-09
		Brian pose la question : If consumption is $11 billion when disposable income is 0 and the marginal propensity to consume is dC/dy = 1/(2y+4)1/2+0.3(in billions of dollars), find the national consumption function. Harley Weston lui répond.
	The average value of a continuous function		2001-05-08
		Esther pose la question : The average value of a continuous function y = f(x) on the interval [a,b] is given by ________________? Harley Weston lui répond.
	Oil revenue		2001-04-21
		Brian pose la question : Suppose that t months from now an oil well will be producing crude oil at the rate of r(t), not a constant, barrels per month and that the price of crude oil will be p(t), not a constant, dollars per barrel. Assume that the oil is sold as soon as it is extracted from the ground. Find an expression for the total revenue from the oil well, R(t). A certain oil well that currently yields 400 barrels of crude oil a month will run dry in 2 years. The price of crude oil is currently $18 per barrel and is expected to rise at a constant rate of 3 cents per barrel per month. What will be the total revenue from this well? {Hint: Model the degraded production rate with the equation: r(t) = (A-Bt)e0.04t} Harley Weston lui répond.
	Integration by parts		2001-04-09
		A student pose la question : how do you integrate x tan-1x dx, i know it can be done by integration by parts maybe, but i'm not sure.... Claude Tardif and Harley Weston lui répond.
	Two integrals		2001-04-03
		Jim pose la question : I'm having trouble with these integrals. Can you help me out? 1)the integral of: x5 arctan x dx 2)the integral of: 2x5 + 9x4 + 19x3 + 13x2 - 5x - 25 ----------------------------------------------- dx x4 + 4x3 + 5x2 Claude Tardif lui répond.
	A jogger		2001-03-12
		Bill pose la question : At time t=0 a jogger is running at a velocity of 300 meters per minute. The jogger is slowing down with a negative acceleration that is directly propotional to time t. This brings the jogger to a stop in 10 minutes. a) write an expression for the velocity of the jogger at time t. b) what is the total distance traveled by the jogger in that 10-minute interval. Harley Weston lui répond.
	How do you integrate secant(theta)?		2000-12-22
		Robert Williamson pose la question : How do you integrate secant(theta)? I know the answer is ln [sec(theta) + tan(theta)] but how do you get there? Claude tardif lui répond.
	A non-integrable function		2000-12-03
		Mark Spilker pose la question : I have a proof that I cannot do here it goes. Let F(x)= 1 if x is a rational number 0 if x is an irrational number Prove the function is not intregrable on the interval (0,1). Hint: Show that no matter how small the norm of the partition, the Riemann Sum for the SigmaNotation F(wi) DeltaiX is not unique. Harley Weston lui répond.
	An integration problem		2000-11-30
		A student pose la question : If a>0 and the integral from b to 0 of 1/(1+x) equals 1/2 the integral from a to 0 of 1/(1+x), express "b" in terms of "a" Claude tardif lui répond.
	Comparing an integral and a sum		2000-11-21
		Douglas Norberg pose la question : A fellow teacher asked me about a problem she wanted to give to her students. It involved whether to take a million dollars or a penny doubled a number of times. I was able to determine the number must have been .01 * 230 which is about $10 million and a lot more than $1 million. To check that I was right I used a spreadsheet and did a Riemann sum. When I finished I reasoned that I had done the task in several steps and I could have done it in 1 step. Thus I integrated .01 * 2x from 0 through 30 but the number I got was $15,490,820.0324. Why the difference? Harley Weston lui répond.
	Dividing a region in half		2000-09-21
		Kerry pose la question : There is a line through the origin that divides the region bounded by the parabola y=x-x2 and the x-axis into two regions with equal area. What is the slope of the line? Penny Nom lui répond.
	Calculus Research Questions		2000-05-22
		William Wright pose la question : I am a Calculus Teacher, and me and my class ran into these two problems without solutions in my manual, we got answers, but are unable to check them. If anyone gets this email and can respond to this with the solutions it be greatly appreciated. . . . Harley Weston lui répond.
	Two calculus problems		2000-05-01
		Kaushal Shah pose la question : How Do WE Integrate the following Functions, Integral xtanx dx How was natural base "e" discovered and why e=2.7....... Claude Tardif lui répond.
	The area of a triangle using calculus		2000-04-15
		Todd Bowie pose la question : Hi, I am not a student but am reviewing calculus for an upcoming interview. I would like to know how to derive the area of a triangle using calculus. Thanks! Patrick Maidorn lui répond.
	Some integration problems		2000-02-23
		Tim Valentine pose la question : I am having a great deal of difficulty with the following integrals, can you help? I think they need the use of trig substitution or integration by parts but I cannot figure out how to begin. Thanks! The integral of 1/(2+3x2) dx. and The integral of x * square root of (4x+5) dx. Harley Weston lui répond.
	Two calculus problems		1999-12-13
		Alan pose la question : I have 2 questions that are very new to me, they were included on a quiz and the material was never covered. Our teacher never explained the purpose and detailed explanation of how to solve the problem. Could you help? Thanks. Question 1: A ball is falling 30 feet from a light that is 50 feet high. After 1 sec. How fast is the shadow of the ball moving towards the light post. Note that a ball moves according to the formula S=16t^2 Question 2: How many trapezoids must one use in order for the error to be less than 10^-8 if we want to find the area under the curve Y=1/X from 1 to 2. Find the exact area, Graph the function and use the trap rule for the "N" that you found. Harley Weston lui répond.
	The area and the circumference of a circle.		1998-08-27
		Jason Wright pose la question : I was looking at the relationship of the area of a circle and the circumference when I realized that 2*pi*r is the derivative of pi*r^2. I was wondering if there is any connective deep dark meaning as to why this appears to be related. Thanks for any help you can give me! Walter Whiteley lui répond.
	Calculus problems		1998-07-13
		Lorraine pose la question : I'm stuck again. Can you help? This involves integration using the method of partial fractions the integral of: 7x(to the 5th) - 2x(cubed) + 3 dx -------------------------------------- x(to the fourth) - 81 Do I have to do long division to reduce the numerator to the fourth power? the integral of: 4- 16x +21x(squared) + 6x(cubed) - 3x(fourth) dx ---------------------------------------------------- x(cubed)(x - 2)(squared) Lorraine Harley Weston lui répond.
	A Calculus Problem		1998-06-28
		Lorraine pose la question : I'm a post-secondary student taking calculus by correspondence. I'm stuck on the following question (and similar ones) Can you help? Evaluate the following indefinite integral: d(theta) ---------- 1 + sin (theta) (It says to multiply both numerator and denominator by: 1 - sin(theta) Thanks Lorraine Harley Weston lui répond.

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