Chapter 13: Q. 39 (page 1004)

Evaluate each of the double integral in the exercise 37-54 as iterated integrals
$\int \int_{R} (2 - 3 x^{2} + y^{3}) d A W h e r e R = {(x, y) | - 3 \leq x \leq 2, 3 \leq y \leq 5}$

Short Answer

Expert verified

The value of the integral is 113.33units

Step by step solution

Given information

We are given an integral

$\int \int_{R} (2 - 3 x^{2} + y^{3}) d A W h e r e R = {(x, y) | - 3 \leq x \leq 2, 3 \leq y \leq 5}$

Use iterated integral

We get,

$\int_{3}^{5} \int_{- 3}^{2} (2 - 3 x^{2} + y^{2}) d x d y = \int_{3}^{5} {[2 x - x^{3} + x y^{2}]}^{2}_{- 3} d y = \int_{3}^{5} (10 - 35 + 5 y^{2}) d y = {[- 25 y + \frac{5}{3} y^{3}]}^{5}_{3} = 113.33 u n i t s$

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Evaluate each of the double integral in the exercise 37-54 as iterated integrals
$\int \int_{R} (2 - 3 x^{2} + y^{3}) d A W h e r e R = {(x, y) | - 3 \leq x \leq 2, 3 \leq y \leq 5}$

Short Answer

Step by step solution

Given information

Use iterated integral

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Evaluate each of the double integral in the exercise 37-54 as iterated integrals ∫∫R(2-3x2+y3)dAWhereR={(x,y)|-3≤x≤2,3≤y≤5}

Short Answer

Step by step solution

Given information

Use iterated integral

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Most popular questions from this chapter

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Evaluate each of the double integral in the exercise 37-54 as iterated integrals
$\int \int_{R} (2 - 3 x^{2} + y^{3}) d A W h e r e R = {(x, y) | - 3 \leq x \leq 2, 3 \leq y \leq 5}$