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

  • Calculus -

    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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