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

1. ## 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)

2. 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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# integral(0 to pie/2)sin^2x/(1 cosx)^2

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