







Integrate (x^2  4x + 4) ^4/3 
20160915 

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. 





Integrate the ((4th root of x^3)+1) dx 
20100412 

Bridget pose la question : integrate the ((4th root of x^3)+1) dx Tyler Wood lui répond. 





The integral of x^x 
20090618 

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 the square root of the sine function 
20090407 

Indrajit pose la question : how to integrate this derivative???
∫√sinx Harley Weston lui répond. 





The volume of a solid 
20080604 

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. 





What is the integral of 13sin^3(x)*cos^7(x)dx? 
20080422 

Cathrine pose la question : I am having trouble integrating this problem. It says to evaluate the integral but I don't know what to do or how to do it.
It is the integral of
13sin^3(x)*cos^7(x)d Harley Weston lui répond. 





Integrate (4+x^2) / (x (2+x)^2) 
20080225 

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. 





The integral of Sqrt(sin x) 
20080124 

tariq pose la question : find integration
Sqrt(sinx) dx , from x=bi/4 to 3bi/4 Harley Weston lui répond. 





Integration 
20080123 

Russell pose la question : how to integrate
1/x ln^2 [x] dx Harley Weston lui répond. 





An integral 
20080123 

Russell pose la question : I checked out the integration site, but would like an explanation for integrating this integral
Tan^3[x] * _dx__
Cos^2[x]
Hope this input is correct!
the part that throws me off is Tan^3[x], if it was squared rather than cubed I would have a easier time
dealing with this one. Harley Weston lui répond. 





Integrate x^8 (x^8 + 2)^2 ((x^8 + 2)^3 + 1)^4 
20070109 

James pose la question : How do you integrate x^8 (x^8 + 2)^2 ((x^8 + 2)^3 + 1)^4 Penny Nom lui répond. 





integral of tan^4 x 
20060514 

Aqil pose la question : integral of tan^{4} x Penny Nom lui répond. 





Integrating e^sin(x) 
20040804 

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 
20030902 

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 
20030625 

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 powerreducing 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. 





Integration of 1/(2+cos(x)) 
20030107 

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/(t^{2}+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 
20020618 

Jeremy pose la question : I am a student at the University of Kansas and I am wondering if there is a general antiderivative 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 
20020417 

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. 





Area between curves 
20010613 

Phil pose la question :
question 1 find the area bound by the curves y = x^{2} + 2x + 3 and y = 2x + 4 question 2 Find the volume generated by rotating the curve x^{2} + y^{2} = 9 about the xaxis Harley Weston lui répond. 





National consumption function 
20010509 

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. 





Oil revenue 
20010421 

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) = (ABt)e^{0.04t}} Harley Weston lui répond. 





How do you integrate secant(theta)? 
20001222 

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. 





Comparing an integral and a sum 
20001121 

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 * 2^{30} 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 * 2^{x} from 0 through 30 but the number I got was $15,490,820.0324. Why the difference? Harley Weston lui répond. 





Calculus Research Questions 
20000522 

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 
20000501 

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 average rate of change of a function 
19990420 

Tammy pose la question : Suppose that the average rate of change of a function f over the interval from x=3 to x=3+h is given by 5e^h4cos(2h). what is f'(3)? I would appreciate any help with this question. Harley Weston lui répond. 





A Calculus Problem 
19980628 

Lorraine pose la question : I'm a postsecondary 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. 

