# Green's theorem

by boneill3
Tags: green, theorem
 P: 127 1. The problem statement, all variables and given/known data Use greens theorem to calculate. $\int_{c}(e^{x}+y^{2})dx+(e^{x}+y^{2})dy$ Where c is the region between y=x2y=x 2. Relevant equations Greens Theorem $\int_{c}f(x.y)dx+g(x,y)dy= \int_{R}\int (\frac{\partial g}{\partial x}-\frac{\partial f}{\partial y})dA$ 3. The attempt at a solution $\frac{\partial g}{\partial x}= 2x$ $\frac{\partial g}{\partial x}= 2y$ Calculate the integral $\int_{0}^{x}\int_{0}^{\sqrt{y}}2x-2y\text{ }dy dx$ $=\frac{x^2}{2}-\frac{4x^{5/2}}{5}$ Does this look right? regards
 P: 161 with f(x,y)=g(x,y)=exp(x)+y*y, dg/dx=exp(x), the second dg/dx is a typo. if you want the region bounded by y=x^2 and y=x, the inside integral must be from x^2 to x and the outside 0 to 1 with area element dydx, the result needs to be a value rather than a function, just something to get use to with multiple integrals.
 P: 127 Thanks $\int_{0}^{1}\int_{x}^{x^2}2x-2y\text{ }dy dx$ $=\frac{1}{30}$ With the outside limits of double integrals eg 0 to 1 do they always have to be constants? regards
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,682 Green's theorem If the result is supposed to be a constant, then, yes, the limits of the integral have to be numbers, not variables!
 P: 127 Thanks

 Related Discussions Calculus 2 Calculus & Beyond Homework 4 Introductory Physics Homework 5 Calculus 4 Calculus 4