What are the limits of integration where C is $\displaystyle \frac{1}{2 }{x}^{ 2} + \frac{1}{4 }{y}^{ 2} = 1$ taken anti-clockwise

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- May 7th 2011, 02:12 AMadam_leedsGreens theorem limits
What are the limits of integration where C is $\displaystyle \frac{1}{2 }{x}^{ 2} + \frac{1}{4 }{y}^{ 2} = 1$ taken anti-clockwise

Thanks - May 7th 2011, 03:14 AMMondreus
Switch to polar coordinates.

http://quicklatex.com/cache3/ql_a66e...d9c265d_l3.png

http://quicklatex.com/cache3/ql_8492...3f4afe8_l3.png

The new area you get is obviously the unit circle which you should know the limits for. - May 8th 2011, 10:31 AMadam_leeds
- May 8th 2011, 12:26 PMMondreus
Almost, but the Jacobian is wrong. http://quicklatex.com/cache3/ql_146c...48c9a97_l3.png