   Chapter 14.6, Problem 18E

Chapter
Section
Textbook Problem

Setting Up a Triple IntegralIn Exercises 13-18, set up a triple integral for the volume of the solid. Do not evaluate the integral.The solid that is the common interior below the sphere z = 4 − x 2 and above the paraboloid z = x 2 + 3 y 2

To determine
The triple integral if the volume of the solid is bounded above the cylinder z=4x2 and below by the paraboloid z=x2+3y2.

Explanation

Given: The solid is bounded above the cylinder z=4x2 and below by the paraboloid z=x2+3y2

Explanation:

The meeting point of two curve is calculated by solving the following equation

4x2=x2+3y24=2x2+3y2

Consider the equation 2x2+3y2=4 if it meets yaxis then y=±42x23

and y=±42x23 meets xaxis then x=±43

Here the limit of the variable z varies from <

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