Chapter 13: Q. 37 (page 1004)

Evaluate each of the double integral in the exercise 37-54 as iterated integrals
$\int \int_{R} (3 - x + 4 y) d A w h e r e R = {(x, y) | 0 \leq x \leq 1, - 1 \leq y \leq 3}$

Short Answer

Expert verified

The value of integral is 26units.

Step by step solution

Given information

We are given an integral as

$\int \int_{R} (3 - x + 4 y) d A w h e r e R = {(x, y) | 0 \leq x \leq 1, - 1 \leq y \leq 3}$

Step 2; Use iterated integrals

We get,

$\int_{- 1}^{3} \int_{0}^{1} (3 - x + 4 y) d x d y = \int_{- 1}^{3} {[3 x - \frac{x^{2}}{2} + 4 x y]}^{1}_{0} d y = \int_{- 1}^{3} [\frac{5}{2} + 4 y] d y = {[\frac{5}{2} y + 2 y^{2}]}^{3}_{- 1} = 26$

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Evaluate each of the double integral in the exercise 37-54 as iterated integrals
$\int \int_{R} (3 - x + 4 y) d A w h e r e R = {(x, y) | 0 \leq x \leq 1, - 1 \leq y \leq 3}$

Short Answer

Step by step solution

Given information

Step 2; Use iterated integrals

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Evaluate each of the double integral in the exercise 37-54 as iterated integrals∫∫R(3-x+4y)dAwhereR={(x,y)|0≤x≤1,-1≤y≤3}

Short Answer

Step by step solution

Given information

Step 2; Use iterated integrals

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Mechanics Maths

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Calculus

Study anywhere. Anytime. Across all devices.

Evaluate each of the double integral in the exercise 37-54 as iterated integrals
$\int \int_{R} (3 - x + 4 y) d A w h e r e R = {(x, y) | 0 \leq x \leq 1, - 1 \leq y \leq 3}$