   Chapter 14.6, Problem 22E

Chapter
Section
Textbook Problem

Volume In Exercises 19-24, use a triple integral to find the volume of the solid bounded by the graphs of the equations. z = 9 − x 3 ,     y = − x 2 + 2 ,       y = 0 ,       z = 0 ,       x ≥ 0

To determine

To calculate: The volume of the solid bounded by with the help of triple integral if the graphs of equations is z=9x3,y=x2+2,y=0,z=0,x0

Explanation

Given: The given equation are z=9x3,y=x2+2,y=0,z=0,x0

Formula used: The Volume of the solid region Q can be calculated by V=Qdxdydz

Calculation:

From the provided equations, it can be concluded that the limit of variable z varies from 0 to 9x3, y varies from 0 to x2+2 and x varies from 0 to 2. Thus the volume of the solid is given by, 020x2+209x3dzdydx=020x2+2[z]09x3dydx=02033x(9x3)dydx=02[(9x3)y]033xdx

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