# Verify Green's Theorem for the line \int_C x d x + y d y, where C is the unit circle, oriented...

## Question:

Verify Green's Theorem for the line {eq}\int_C x d x + y d y, {/eq} where C is the unit circle, oriented counterclockwise

## Green's Theorem:

We will {eq}\oint F_{1}dx+F_{2}dy=\int \int \left ( \frac{\partial F_{2}}{\partial x}-\frac{\partial F_{1}}{\partial y} \right )dxdy {/eq} solve the problem using Green's Theorem here we will change the equation of circle to parametric form to solve the left side.

## Answer and Explanation: 1

Become a Study.com member to unlock this answer! Create your account

To solve the problem we will use Green's Theorem:

{eq}\oint F_{1}dx+F_{2}dy=\int \int \left ( \frac{\partial F_{2}}{\partial x}-\frac{\partial...

See full answer below.

#### Learn more about this topic:

The Fundamental Theorem of Calculus

from

Chapter 12 / Lesson 10
7.4K

The fundamental theorem of calculus is one of the most important points to understand in mathematics. Learn to define the formula of the fundamental theorem of calculus and explore examples of it put into practice.