Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 16 - Multiple Integration - 16.2 Double Integrals over More General Regions - Exercises - Page 859: 39


$\dfrac{e^{16}-1}{4} $

Work Step by Step

The domain $D$ for given region can be expressed as: $0 \leq x \leq 4$ and $\dfrac{x}{4} \leq y \leq \dfrac{3x}{4}$ The iterated integral can be calculated as: $\iint_{D} f(x,y) d A=\int_0^4 \int_{x/4}^{3x/4} e^{x^2} dy dx\\=\int_0^4 (ye^{x^2})_{x/4}^{3x/4} dx \\=\int_0^4 [\dfrac{3x}{4}e^{x^2}-\dfrac{x}{4}e^{x^2}] \ dx \\=\dfrac{1}{4}[e^{x^2}]_0^4\\=\dfrac{e^{16}-1}{4} $
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