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October 1, 2014

October 1, 2014

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

Evaluate the integral xsqrt(100-x^2dx) for the interval (0,10)

- Calculus -
**Steve**, Sunday, February 10, 2013 at 7:26pmlet 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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