   Chapter 15, Problem 22RE

Chapter
Section
Textbook Problem

Calculate the value of the multiple integral.22. ∬ D x y   d A , where D = {(x, y) | 0 ≤ y ≤ 1, y2 ≤ x ≤ y + 2}

To determine

To calculate: The value of given double integral over the region R.

Explanation

Given:

The rectangular region is, D={(x,y)|0y1,y2xy+2} .

Calculation:

Integrate with respect to x and apply the limit.

DxydA=01y2y+2xydxdy=01[yx22]y2y+2dy=01(y(y+2)22y(y2)22)dy=01(y(y2+4+4y)2yy42)dy

= DxydA=1201(y3+4y+4y2y5)dy

Integrate with respect to y and apply the limit

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