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)
So the problem is $\displaystyle \int_0^{\pi/2} \frac{cos(x)}{\sqrt{1+ sin^2(x)}} dx$?
Let u= sin(x) so that du= cos(x)dx. When x=0, u= 0 and when $\displaystyle x= \pi/2$, u= 1 so the problem becomes $\displaystyle \int_0^1 \frac{1}{\sqrt{1+ u^2}} du$.
Now, use a trig substitution to do that- remembering that $\displaystyle 1+ tan^2(\theta)= sec^2(\theta)$.
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.