Chapter 13: Q. 36 (page 1004)

Evaluate each of the integrals in exercise 33-36 as iterated integrals and then compare your answers with those you found in exercise 29-32
$\int \int_{R} x^{2} y^{3} d A W h e r e R = {(x, y) | 1 \leq x \leq 3, 0 \leq y \leq 2}$

Short Answer

Expert verified

The value of the integral is $\frac{104}{3}$

Step by step solution

Given information

We are given an integral

$\int \int_{R} x^{2} y^{3} d A W h e r e R = {(x, y) | 1 \leq x \leq 3, 0 \leq y \leq 2}$

Use iterated integral

We get,

$\int_{0}^{2} \int_{1}^{3} x^{2} y^{3} d x d y = \int_{0}^{2} {[\frac{x^{3} y^{3}}{3}]}^{3}_{1} d y = \int_{0}^{2} [\frac{26 y^{3}}{3}] d y = {[\frac{26}{12} y^{4}]}^{2}_{0} = \frac{104}{3}$

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Evaluate each of the integrals in exercise 33-36 as iterated integrals and then compare your answers with those you found in exercise 29-32
$\int \int_{R} x^{2} y^{3} d A W h e r e R = {(x, y) | 1 \leq x \leq 3, 0 \leq y \leq 2}$

Short Answer

Step by step solution

Given information

Use iterated integral

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Evaluate each of the integrals in exercise 33-36 as iterated integrals and then compare your answers with those you found in exercise 29-32∫∫Rx2y3dAWhereR={(x,y)|1≤x≤3,0≤y≤2}

Short Answer

Step by step solution

Given information

Use iterated integral

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Statistics

Mechanics Maths

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Evaluate each of the integrals in exercise 33-36 as iterated integrals and then compare your answers with those you found in exercise 29-32
$\int \int_{R} x^{2} y^{3} d A W h e r e R = {(x, y) | 1 \leq x \leq 3, 0 \leq y \leq 2}$