Chapter 13: Q.33 (page 1004)

Evaluate Each of the integrals in exercises 33-36 as an iterated integral and then compare your answer with thoise you found in exercise 29-32
$\int \int_{R} x y d A W h e r e R = {(x, y) | 0 \leq x \leq 2, 1 \leq y \leq 4}$

Short Answer

Expert verified

The value of integral is $\int \int_{R} x y d A W h e r e R = {(x, y) | 0 \leq x \leq 2, 1 \leq y \leq 4}$ is 15units

Step by step solution

Given information

We have given an integral $\int \int_{R} x y d A W h e r e R = {(x, y) | 0 \leq x \leq 2, 1 \leq y \leq 4}$

Using iterated integral

Using the definition of iterated integrals we get,

$\int_{1}^{4} \int_{0}^{2} x y d x d y = \int_{1}^{4} {[\frac{x^{2} y}{2}]}^{2}_{0} d y = \int_{1}^{4} 2 y d y = {[y^{2}]}^{4}_{1} = 16 - 1 = 15$

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Evaluate Each of the integrals in exercises 33-36 as an iterated integral and then compare your answer with thoise you found in exercise 29-32
$\int \int_{R} x y d A W h e r e R = {(x, y) | 0 \leq x \leq 2, 1 \leq y \leq 4}$

Short Answer

Step by step solution

Given information

Using iterated integral

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Evaluate Each of the integrals in exercises 33-36 as an iterated integral and then compare your answer with thoise you found in exercise 29-32∫∫RxydAWhereR={(x,y)|0≤x≤2,1≤y≤4}

Short Answer

Step by step solution

Given information

Using iterated integral

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Probability and Statistics

Mechanics Maths

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Evaluate Each of the integrals in exercises 33-36 as an iterated integral and then compare your answer with thoise you found in exercise 29-32
$\int \int_{R} x y d A W h e r e R = {(x, y) | 0 \leq x \leq 2, 1 \leq y \leq 4}$