Answer
$$176$$
Work Step by Step
Volume, $$V=\int_{0}^{2} \int_{1}^{4} x^2+4y^2 \ dy \ dx =\int_{0}^{2} (x^2y+\dfrac{4y^3}{3})_1^4 \ dx =\int_0^2 [3x^2 +84] \ dx =(x^3+84x)_0^2 =8+168=176$$
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 15 - Multiple Integrals - Review - Exercises - Page 1103: 35
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