Hello,
I have my final tomorrow and not sure how to tackle this question, another polar coordinates problem!?
$\displaystyle \int_{0}^{\frac{\pi}{2}}\int_{0}^{\cos \theta}e^{\sin \theta} drd\theta$
$\displaystyle \int_{0}^{\frac{\pi}{2}}\int_{0}^{\cos \theta}e^{\sin \theta} \, dr \, d\theta = \int_{0}^{\frac{\pi}{2}} \left[r e^{\sin \theta}\right]_0^{\cos \theta} \, d\theta = \int_{0}^{\frac{\pi}{2}} \cos \theta \, e^{\sin \theta} \, d\theta$
and this integral is easily done using a simple substitution.