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Math Help - Finding an integral from a derivative.

  1. #1
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    Finding an integral from a derivative.

    Differentiate tan^{-1}(cos x) and hence evaluate \int_0^\pi sin \frac{dx}{(2-sin^{2}x)}
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  2. #2
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    Quote Originally Posted by nerdzor View Post
    Differentiate \tan^{-1}(\cos x) and hence evaluate \int_0^\pi {\color{red}\sin x} \frac{dx}{(2 - \sin^{2}x)}
    You have a made a typo (see the red).

    Can you differentiate the given function? Note that 1 + \cos^2 x = 2 - \sin^2 x using the Pythagorean Identity. So the derivative of the function is equal to the integrand. What does that tell you ....?
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