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Math Help - evaluating integrals - a and x

  1. #1
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    evaluating integrals - a and x

    Hi I am not sure what to do with this one

    Evaluate the following integral

    definite integral sign b="a" ; a=0 ( x )* ("a"^2 - x^2)^1/2 dx

    where "a" is a positive constant

    I know the x must be x^2 on the other side but I really don't know what to do with this mess.

    Directions please

    This calculus beginner
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  2. #2
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    Quote Originally Posted by calcbeg View Post
    Hi I am not sure what to do with this one

    Evaluate the following integral

    definite integral sign b="a" ; a=0 ( x )* ("a"^2 - x^2)^1/2 dx

    where "a" is a positive constant

    I know the x must be x^2 on the other side but I really don't know what to do with this mess.

    Directions please

    This calculus beginner
    \int_0^a x\sqrt{a^2-x^2} \, dx

    substitution ... let u = a^2 - x^2

    du = -2x \, dx

    -\frac{1}{2} \int_0^a -2x\sqrt{a^2-x^2} \, dx

    substitute and reset the limits of integration ...

    -\frac{1}{2} \int_{a^2}^0 \sqrt{u} \, du

    \frac{1}{2} \int_0^{a^2} \sqrt{u} \, du

    integrate and evaluate the last definite integral using the FTC
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