Chapter 16.6, Problem 39E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the area of the surface.

**39.** The part of the plane 3*x* + 2*y* + *z* = 6 that lies in the first octant

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.

**Formula used:**

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

Write the expression to find area of triangular region with base and height.

Here,

Write the equation of plane as follows.

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

The function
*xy*-plane when

Substitute 0 for

The function
*xy*-plane in the line

**Calculation of x-intercept:**

Substitute 0 for *y* in equation (4),

**Calculation of y-intercept:**

Substitute 0 for *x* in equation (4),

From the given data, it is clear that, *D* is a triangular region with base as *x*-intercept and height as *y*-intercept.

**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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