   Chapter 15.2, Problem 10E

Chapter
Section
Textbook Problem

Evaluate the double integral.10. ∬ D y x 2 − y 2 d A ,   D = { ( x , y ) | 0 ≤ x ≤ 2 , 0 ≤ y ≤ x }

To determine

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

Explanation

Given

The domain is, D={(x,y)|0x2,0yx} .

Calculation:

First, compute the integral with respect to y.

Dyx2y2dA=02[0x12.2yx2y2dy]dx=02[0x12.x2tdt]dx=02[(1)2.23(x2t)32]0xdx=02[13(x2y2)32<

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