Chapter 13: Q. 40 (page 1004)

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

Short Answer

Expert verified

The value of integral is $e^{2} - e^{- 2}$

Step by step solution

Given information

We are given an integral

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

use iterated integral

We get,

$\int_{- 2}^{2} \int_{- 3}^{2} (x - e^{y}) d x d y = \int_{- 2}^{2} {[\frac{x^{2}}{2} - x e^{y}]}^{2}_{- 3} d y = \int_{- 2}^{2} (- \frac{5}{2} + e^{y}) d y = {[- \frac{5}{2} y + e^{y}]}^{2}_{- 2} = e^{2} - e^{- 2}$

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

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(x-ey)dAWhereR={(x,y)|-3≤x≤2,-2≤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

Geometry

Probability and Statistics

Pure Maths

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Study anywhere. Anytime. Across all devices.

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