Chapter 15, Problem 45RE

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the area of the part of the surface *z* = *x*^{2} + *y* that lies above the triangle with vertices (0, 0), (1, 0), and (0, 2).

To determine

**To find:** The area of the given region.

Explanation

**Formula used:**

The surface area with equation

Here, *D* is the given region.

**Property used:**

**Given:**

The part of the surface

**Calculation:**

From the given conditions, it is observed that the equations of the triangle are *x* varies from 0 to 1.

The partial derivatives

Then, by the formula mentioned above, the area of the surface is given by,

Integrate with respect to *y* and apply the limit of it.

Integrate with respect to *x*. To integrate the second integrand, substitute

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