Chapter 16.6, Problem 41E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Find the area of the surface.

**41.** The part of the plane *x* + 2*y* + 3*z* = 1 that lies inside the cylinder *x*^{2} + *y*^{2} = 3

To determine

**To find:** The area for the surface of the part of the plane

Explanation

**Given data:**

The equation of the part of the plane is given as follows.

Rearrange the equation.

The equation of the cylinder is given as follows.

**Formula used:**

Write the expression to find the surface area of the plane.

Write the expression to find base surface area of cylinder with radius.

Here,

Write the equation of plane as follows.

Consider *x* and *y* as parameters and parameterize the plane as follows.

**Calculation of**
**:**

Take partial derivative for equation (1) with respect to *x*.

**Calculation of**
**:**

Take partial derivative for equation (1) with respect to *y*

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