Question

Calculate the integral, if it converges. You may calculate the limit by appealing to the dominance of one function over another, or by l'Hopital's rule.

The integral is sinx/sqrt(cosx) from pi/4 to pi/2. How do i solve this?

Answer 1

\[\int\limits_{\pi/4}^{\pi/2} \sin(x)/\sqrt \cos(x)\]

Answer 2

since cos(pi/2) = 0, we have
\[\lim t \rightarrow \pi/2 \int\limits_{\pi/4}^{t} \sin(x)/\sqrt{\cos(x)} dx\]

Answer 3

to do the integral, set u = cos(x), du = -sin(x) dx

Answer 4

can take it from here?

Answer 5

yep, i got it! \[2\sqrt(\sqrt(2)/2\]
thanks!