double integral using polar coordinates

**Robb** · June 18th 2009, 12:34 AM

Hello,
I have my final tomorrow and not sure how to tackle this question, another polar coordinates problem!?

$\int_{0}^{\frac{\pi}{2}}\int_{0}^{\cos \theta}e^{\sin \theta} drd\theta$

**mr fantastic** · June 18th 2009, 01:07 AM

Originally Posted by Robb

Hello,
I have my final tomorrow and not sure how to tackle this question, another polar coordinates problem!?

$\int_{0}^{\frac{\pi}{2}}\int_{0}^{\cos \theta}e^{\sin \theta} drd\theta$

$\int_{0}^{\frac{\pi}{2}}\int_{0}^{\cos \theta}e^{\sin \theta} \, dr \, d\theta = \int_{0}^{\frac{\pi}{2}} \left[r e^{\sin \theta}\right]_0^{\cos \theta} \, d\theta = \int_{0}^{\frac{\pi}{2}} \cos \theta \, e^{\sin \theta} \, d\theta$

and this integral is easily done using a simple substitution.

**Robb** · June 18th 2009, 01:14 AM

lol.. shows you how tiried I am, not the best to be doing maths when sleep deprived. I totally missed that! thanks allot :P

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