Rayan's question at Yahoo! Answers (Green's Theorem)

MHB Math Helper

Fernando Revilla

Well-known member
MHB Math Helper
Hello Rayan,

Easily proved, $C:r=2\cos \theta$ is the circle $Cx-1)^2+y^2=1$. If $D$ is the disk with boundary $C$, then by the Green's theorem, $$W=\int_C(e^x − 9y)dx + (e^y + 4x)dy=\iint_D(Q_x-P_y)dxdy=\iint_D(4+9)dxdy\\=13\iint_Ddxdy=13\mbox{Area }(D)=13\cdot \pi\cdot 1^2=\boxed{\;13\pi\;}$$
If you have further questions you can post them in the Calculus section.