- #1
boneill3
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Homework Statement
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=x2y=x
Homework 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]
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