Chapter 16.4, Problem 28E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Calculate ∫_{C}**F** · *d***r**, where **F**(*x*, *y*) = ⟨*x*^{2} +* y*, 3*x* − *y*^{2}⟩ and *C* is the positively oriented boundary curve of a region *D* that has area 6.

To determine

**To calculate**: The value of

Explanation

**Given data:**

Field vector is

**Formula used:**

**Greenâ€™s Theorem:**

Consider a positively oriented curve *C* which is piece-wise smooth, simple closed curve in plane with region *D*. Then the line integration of vector field
*C* is,

Here,

*A* is area,

*P*,

*Q*, and

*P* and *Q* have continuous partial derivatives.

Compare the two vector fields

Find the value of

Take partial differentiation for equation (2) with respect to *y*.

Find the value of

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