   Chapter 15.2, Problem 27E

Chapter
Section
Textbook Problem

Find the volume of the given solid.27. The tetrahedron enclosed by the coordinate planes and the plane 2x + y + z = 4

To determine

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

Explanation

Given:

The coordinate planes are, 2x+y+z=4 .

Formula used:

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

Calculation:

The plane equation can be modified as y=42xy and it is observed from the given equation of plane that y varies from 0 to 42x and x varies from 0 to 2. Thus, the volume of the solid is computed as follows.

V=RzdA=02042x(42xy)dydx

First, compute the integral with respect to y.

V=02[4y2xyy22]042xdx

Apply the limit value for y,

V=02[(4(42x)2x(42x)(42x)22)(000)]

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