Greens Theorem: Region with a Hole Let be the region inside the circle and outside the

Chapter 15, Problem 43

(choose chapter or problem)

Let R be the region inside the circle \(x=5 \cos \theta, y=5 \sin \theta\) and outside the ellipse

\(x=2 \cos \theta, y=\sin \theta\). Evaluate the line integral

\(\int_{C}\left(e^{-x^{2} / 2}-y\right) d x+\left(e^{-y^{2} / 2}+x\right) d y\)

where \(C=C_{1}+C_{2}\) is the boundary of R, as shown in the figure.

Text Transcription:

x = 5 cos theta, y = 5 sin theta

x =2 cos theta, y = sin theta

int_C (e^{-x^2 / 2 - y) dx + (e^{-y^2/2} + x) dy

C = C_1+ C_2