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166 Answered Questions for the topic Integration



How do i know which part of the function i should integrate and which one to derivate when doing integration by parts?

As in, which one should i label as f(x) and which is g(x)? How should i think when i see a problem given?
Integration Calculus Integrals


What is the volume of the surface intercepted by x^2+y^2=1 , z=2-|x| , z=0 ?

triple integrals
Integration Math Help


How do you integrate 1/(x^2 + 25)^2?

I've been stuck on this question for a while. I've tried integration by parts but that doesn't help so I thought substitution would help but I don't know what to substitute it for.
Integration Calculus U Substitution


integrate using "reversed" substitution

Using the substitution x=(√3)tany find the exact value of1∫3 1/√(3+x^2) dxexpressing your answer as a single logarithm in terms of y


Integrate x/(x^2-5x+25)

When I substitute u=x^2-5x+25 I get du=2x-5 dx. That gets me close to x dx. I would normally just pull out 1/2, but I'm confused how to deal with the -5.  it looks like I should get a ln portion... more
Integration Calculus Pre Calculus


A curve is such that dy/dx= 6/x^2 and (2,9) is a point on the curve. Find the equation of the curve.

The slope of the curve has to be found by the dy/dx= 6/x^2. It will most likely end up as a y-y1=m(x-x1) formula at the end. 
Integration Volume By Integration


find the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=9+x^7 about the y axis

find the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=9+x^7 about the y axis


can someone help me integrate the following?

∫(secθ⁄cosθ) dθ


Let f(x) = integral from (-2) to (x^2-3x) of e^(t^2) dt. At what value of x is f(x) a minimum?

At what value of x is f(x) a minimum?   I know f'(x) = e^((x^2-3x)^2) , but I don't know how to continue.   Thanks!


integral of dx/root of c-k/x

Integration Calculus


Find the interest earned on an interest-bearing account

Every month, a particular interest-bearing account earns 0.2 percent interest on the average balance for that month. The function B(t) =7.5t^2 -300t +5000 represents one investor's balance in this... more
Integration Integral


Why is the derivative of the answer to an integral equal to the primary function which we want to take integral of? I'm looking for the concept.

I'm in a hurry to find the answer. Please help me. Thanks so much
Integration Calculus Integral



Integration Calculus Substitution


I need help on integration problems

∫cos4 θ sin θ dθ



find integration by subtutitions.
Integration Calculus Integrals


How do you find the equation to an integral when the equation is not given but the answer to the integral is?

int; integral sign Find int (bottom: -3 top: -5.5) (8*f(x)-9)dx when int (bottom:-5.5 top:-3) f(x)dx = -2 Also; let int (bottom: -8 top: -0.5) f(x)dx =8 int (bottom: -8 top: -5.5) f(x)dx =... more
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