Chapter 16.4, Problem 2E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Evaluate the line integral by two methods: (a) directly and (b) using Green’s Theorem.

**2.** `∮`

_{C}*y dx* − *x dy*,

*C* is the circle with center the origin and radius 4

**(a)**

To determine

**To evaluate**: the line integral in direct method.

Explanation

**Given data:**

Line integral is
*C* is circle with center the origin and radius 4.

**Formula used:**

Write the equation of circle with center the origin.

Consider parametric equations of curve *C*,

Substitute
*x*,
*y*, and 4 for *r* in equation (1).

The LHS equal to the RHS. Hence, the parametric equations represent a curve circle *C* with origin as center and radius 4.

Differentiate equation (2) with respect to *t*.

Differentiate equation (3) with respect to *t*.

Find the value of line integral

**(b)**

To determine

**To evaluate**: The line integral using Green’s Theorem.

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