iterated integral

[mathstresser]

Evaluate the iterated integral by converting to polar coordinates.
1 (2-y^2)^(1/2)
∫∫ (x+y) dxdy
0 y

x+y= rcos theta + r sin theta

I change it to
(2-(rsin theta)^2)^(1/2)
∫∫(r^2)(cos theta +sin theta) drdtheta
sin theta

But I don't know what to evaluate the outside integral at.

Is the rest of it right?

27

 

[galactus]

mathstresser, you should really try to learn a little LaTex. Is this your integral?.

Click on quote at the upper right hand corner of this post to see the code I used. Give it a shot.

\(\displaystyle \L\\\int_{0}^{1}\int_{y}^{\sqrt{2-y^{2}}}(x+y)dxdy\)


Polar:

\(\displaystyle \L\\\int_{0}^{\frac{\pi}{4}}\int_{0}^{\sqrt{2}}r^{2}(cos({\theta})+sin({\theta}))drd{\theta}\)

 

[mathstresser]

Thanks!