   Chapter 15.2, Problem 7E

Chapter
Section
Textbook Problem

Evaluate the double integral.7. ∬ D y x 2 + 1 d A ,   D = { ( x , y ) | 0 ≤ x ≤ 4 , 0 ≤ y ≤ x }

To determine

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

Explanation

Given

The domain is, D={(x,y)|0x4,0yx} .

Calculation:

First, compute the integral with respect to y.

Dyx2+1dA=04[0xyx2+1dy]dx=041x2+1.[y22]0xdx

Apply the limit value for y,

Dyx2+1dA=1204(x)202x2+1dx=1204x

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