   Chapter 15.2, Problem 8E

Chapter
Section
Textbook Problem

Evaluate the double integral.8. ∬ D ( 2 x + y ) d A ,   D = { ( x , y ) | 1 ≤ y ≤ 2 , y − 1 ≤ x ≤ 1 }

To determine

To calculate: The value of given double integral over D .

Explanation

Given

The domain is, D={(x,y)|1y2,y1x1} .

Calculation:

First, compute the integral with respect to x.

D(2x+y)dA=12[y11(2x+y)dx]dy=12[2x22+xy]y11dy=12[x2+xy]y11dy

Apply the limit value for x,

D(2x+y)dA=12[(12+(1)y)((y1)2y(y1))]dy=12[(1+y)((y1)

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