Chapter 16, Problem 31RE

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Verify that Stokes’ Theorem is true for the vector field **F**(*x*, *y*, *z*) = *x ^{2}*

To determine

**To verify:** The Stokes’ Theorem is true for the vector field

Explanation

**Given data:**

**Formula used:**

Write the expression for Stokesâ€™ Theorem.

Write the expression for

Consider the expression as follows.

Write the expression for

Compare equations (3) and (4).

Substitute

Find the value of

Since, the paraboloid lies above the *xy*-plane , the value of

Consider the expression for part of the paraboloid as follows.

Substitute

Write the expression for circle.

Compare equations (6) and (7)

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