Answer
True.
Work Step by Step
As $y$ is bounded by $y=g_{2}(x)$ and $y=g_{1}(x),$ we should have $g_{1}(x) \leq y \leq g_{2}(x)$
\[
\int_{a}^{b} \int_{g_{1}(x)}^{g_{2}(x)} f(x, y) d y d x=\iint_{R} f(x, y) d A
\]
Calculus, 10th Edition (Anton)
by Anton, Howard
Published by
Wiley
ISBN 10:
0-47064-772-8
ISBN 13:
978-0-47064-772-1
Chapter 14 - Multiple Integrals - 14.2 Double Integrals Over Nonrectangular Regions - Exercises Set 14.2 - Page 1016: 34
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