   Chapter 15, Problem 35RE

Chapter
Section
Textbook Problem

Find the volume of the given solid.35. Under the paraboloid z = x2 + 4y2: and above the rectangle R = [0, 2] × [1, 4]

To determine

To find: The volume of the given solid.

Explanation

Given:

The region R lies under the paraboloid z=x2+4y2 and above the rectangle R=[0,2]×[1,4] .

Formula used:

The volume of the given solid is given by, V=RdA .

Calculation:

The volume of the given solid is,

V=RdA=0214(x2+4y2)dydx

Integrate with respect to y and apply the limit.

V=0214(x2+4y2)dydx=02[x2y+4y33]14dx=02[(x2(4)+4(4)33)(x2(1)+4(1)33)</

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