Thursday
December 5, 2013

Homework Help: Calculus

Posted by Sammy on Sunday, February 10, 2013 at 7:19pm.

Given a function f(x)=sqrt(100-x^2)
Evaluate the integral xsqrt(100-x^2dx) for the interval (0,10)

• Calculus - Steve, Sunday, February 10, 2013 at 7:26pm

let x = 10sinθ. then
dx = 10cosθ dθ
√(100-x^2) = √(100-100sin^2θ = 10√(1-sin^2θ) = 10cosθ

The integral then becomes

∫(10cosθ)(10cosθ dθ) = 100∫cos^2 θ dθ

which I'm sure you can do.
The limits of integration then become
0<=x<=10 --> 0 <= θ <= π/2

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