A volume integral Find the volume of the solid D bounded by theparaboloids y = x2 + 3z2 + 1 and y = 5 - 3x2 - z2 Inner integralwith respect to yZAy = x2 + 3z2 + 1y = 5 – 3x2 – 2Rу(5-3x2-7Volume = [[(dy+3+1R(a)Figure 16.44

Given: Paraboloids y=x2+3z2+1, y=5-3x2-z2To find: The volume of the solid D bounded by the given…

Answered: Inner integral with respect to y ZA y =…

Inner integral with respect to y ZA y = x2 + 3z2 + 1 y = 5 – 3x2 – 2 R у (5-3x2-7 Volume = [[( dy +3+1 R (a) Figure 16.44

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

A volume integral Find the volume of the solid D bounded by the
paraboloids y = x² + 3z² + 1 and y = 5 - 3x² - z²

Inner integral
with respect to y
ZA
y = x2 + 3z2 + 1
y = 5 – 3x2 – 2
R
у
(5-3x2-7
Volume = [[(
dy
+3+1
R
(a)
Figure 16.44

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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