xy? and above the area bounded by x = y? Find the volume of the region under the surface z = and x + 3y = 4

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 40E: Find the exact volume of the solid that results when the region bounded in quadrant I by the axes...
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This is a calculus 3 problem. Please explain clearly, no cursive writing.

xy? and above the area bounded by x =
Find the volume of the region under the surface z =
and x + 3y = 4
Transcribed Image Text:xy? and above the area bounded by x = Find the volume of the region under the surface z = and x + 3y = 4
Expert Solution
Step 1

The surface is z=xy2. The region is bounded by x=y2 and x+3y=4.

Find the limit of the region as follows.

The limit of x are x=y2 to x=4-3y.

The limit of y  are obtained as follows.

y2=4-3yy2+3y-4=0(y+4)(y-1)=0y=-4,1

The the limits of the regions are -4y1 and y2x4-3y.

 

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