Question
Area as a line integral Show that if $R$ is a region in the plane bounded by a piecewise smooth, simple closed curve $C,$ then$$\begin{array}{l}{\text {Area of}}\end{array}R=\oint_{C} x d y=-\oint_{C} y d x$$
Step 1
Step 1: We start by noting that the area of a region $R$ in the plane can be expressed as a double integral over the region $R$: $$\text{Area of } R = \iint_R dA$$ Show more…
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