   Chapter 15.1, Problem 41E

Chapter
Section
Textbook Problem

Find the volume of the solid enclosed by the surface z = 1+ x2yey and the planes z = 0, x = ±1, y = 0, and y = 1.

To determine

To find: The volume of the solid that enclosed by the surface and the planes.

Explanation

Calculation:

Formula used:

The volume of the solid, V=RzdA , where, z is the given function.

Given:

The surface is z=1+x2yey .

The planes are z=0,y=0,y=1 and x=±1 .

Calculation:

The rectangular region is R=[1,1]×[0,1] .

The volume of the solid is,

V=RzdA=0111(1+x2yey)dxdy

First, compute the integral with respect to x.

V=01[x+x3yey3]11dy

Apply the limit value for x,

V=01[(1+13yey3)(1(1)3yey3)]dy=01[(1+yey3)(1

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