Chapter 16, Problem 27RE

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Evaluate the surface integral.

**27.** ∬* _{S} z dS*, where

To determine

**To Evaluate:** The surface integral of

Explanation

**Given data:**

**Formula used:**

Write the expression for surface integral.

Write the expression for

Write the expression for

Write the required differentiation formulae.

Consider the expression as follows.

Differentiate equation (4) with respect to

Differentiate equation (4) with respect to

Substitute

Substitute

Modify equation (1) as follows.

Substitute
*z* and

Find the value of limits as follows.

Consider the circle equation as follows.

Write the expression for circle equation.

Compare equation (6) and (7).

Area of circle depends upon radius

Substitute

Apply limits and modify equation as follows.

Simplify equation as follows.

Consider the expression for

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