(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use greens theorem to calculate.

[itex]\int_{c}(e^{x}+y^{2})dx+(e^{x}+y^{2})dy[/itex]

Where c is the region between y=x^{2}y=x

2. Relevant equations

Greens Theorem

[itex]\int_{c}f(x.y)dx+g(x,y)dy= \int_{R}\int (\frac{\partial g}{\partial x}-\frac{\partial f}{\partial y})dA[/itex]

3. The attempt at a solution

[itex]\frac{\partial g}{\partial x}= 2x[/itex]

[itex]\frac{\partial g}{\partial x}= 2y[/itex]

Calculate the integral

[itex]\int_{0}^{x}\int_{0}^{\sqrt{y}}2x-2y\text{ }dy dx[/itex]

[itex]=\frac{x^2}{2}-\frac{4x^{5/2}}{5}[/itex]

Does this look right?

regards

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# Green's theorem

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