   Chapter 15, Problem 23RE

Chapter
Section
Textbook Problem

Calculate the value of the multiple integral.23. ∬ D y 1 +   x 2   d A , where D is bounded by y   =   x , y = 0, x = 1

To determine

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

Explanation

Given:

The region D is bounded by y=x,y=0,x=1 .

Calculation:

From the given conditions, it is observed that x varies from 0 to 1 and y varies from 0 to x .

First, compute the integral with respect to y.

Dyx2+1dA=01[0xyx2+1dy]dx=011x2+1.[y22]0xdx

Apply the limit value for y,

Dyx2+1dA=1201(x)202x2+1dx=1201

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