# double integral using polar coordinates

• Jun 18th 2009, 12:34 AM
Robb
double integral using polar coordinates
Hello,
I have my final tomorrow and not sure how to tackle this question, another polar coordinates problem!?

$\displaystyle \int_{0}^{\frac{\pi}{2}}\int_{0}^{\cos \theta}e^{\sin \theta} drd\theta$
• Jun 18th 2009, 01:07 AM
mr fantastic
Quote:

Originally Posted by Robb
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.
• Jun 18th 2009, 01:14 AM
Robb
lol.. shows you how tiried I am, not the best to be doing maths when sleep deprived. I totally missed that! thanks allot :P