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Chapter 13: Q. 40 (page 1004)

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

Expert verified

The value of integral ise2-e-2

Step by step solution

01

Given information

We are given an integral

∫∫R(x-ey)dAWhereR={(x,y)|-3≤x≤2,-2≤y≤2}

02

use iterated integral

We get,

∫-22∫-32(x-ey)dxdy=∫-22[x22-xey]2-3dy=∫-22(-52+ey)dy=[-52y+ey]2-2=e2-e-2

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∫01 ∫06−y ∫03−3y−(1/2)z (y−z)dxdzdy

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