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Chapter 13: Q. 14 (page 1003)

Explain why using an iterated integral to evaluate a double integral is often easier than using the definition of the double integral to evaluate the integral.

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Earlier in this section, we showed that we could use Fubini’s theorem to evaluate the integral $\int \int_{R} x^{2} y d A$ and we showed that $\int_{2}^{5} \int_{1}^{3} x^{2} y d x d y = 91$ Now evaluate the double integral by evaluating the iterated integral $\int_{1}^{3} \int_{2}^{5} x^{2} y d y d x$ .

Discuss the similarities and differences between the definition of the double integral found in Section $13.1$ and the definition of the triple integral found in this section.

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Explain why using an iterated integral to evaluate a double integral is often easier than using the definition of the double integral to evaluate the integral.

Short Answer

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Step 1. Given information:

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