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Math Help - integral (0 to pi/2) cosx/sqrt(1+sin^2x) help?

  1. #1
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    integral (0 to pi/2) cosx/sqrt(1+sin^2x) help?

    I stumbled upon this question in my text book,
    could someone help me solve it?

    integral (0 to pi/2) cosx/sqrt(1+sin^2x)
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  2. #2
    MHF Contributor

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    So the problem is \int_0^{\pi/2} \frac{cos(x)}{\sqrt{1+ sin^2(x)}} dx?

    Let u= sin(x) so that du= cos(x)dx. When x=0, u= 0 and when x= \pi/2, u= 1 so the problem becomes \int_0^1 \frac{1}{\sqrt{1+ u^2}} du.

    Now, use a trig substitution to do that- remembering that 1+ tan^2(\theta)= sec^2(\theta).

    Since I am first getting rid of trig functions, and then introducing trig functions, you could probably do this with a single trig identity, but that is how I would handle it.
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