   Chapter 14, Problem 56RE

Chapter
Section
Textbook Problem

VolumeIn Exercises 55 and 56, use a triple integral to find the volume of the solid bounded by the graphs of the equations. z = 8 − x − y ,     z = 0 ,   y = x ,     y = 3 ,     x = 0

To determine

To calculate: The volume of z=8xy,z=0,y=x,y=3,x=0 for the solid bounded by graphs

Explanation

Given:

The solid is bounded by graphs z=8xy,z=0,y=x,y=3,x=0.

Formula used:

Integration formula:

abxndx=[xn+1n+1]ab

Volume of a solid:

V=y1y2x1x2z1z2dzdxdy

Calculation:

We consider the solid bounded by graph,

Apply the formula for volume of solid,

V=y1y2x1x2z1z2dzdxdy

As can be seen from above formula

x1=0,x2=yy1=0,y2=3z1=0,z2=8xy

∴,

V=y1y2x1x2z1z2dzdxdy=030y08xydzdxdy

Assume remaining variable constant and integrate the provided expression with respect to z

030y08xydzdxd<

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