   Chapter 15, Problem 24RE

Chapter
Section
Textbook Problem

Calculate the value of the multiple integral.24. ∬ D y 1 +   x 2   d A , where D is the triangular region with vertices (0, 0), (1, 1), and (0, 1)

To determine

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

Explanation

Given:

The region D is the triangle with vertices (0,0),(1,1),(0,1) .

Calculation:

From the given conditions, it is observed that the equations of the sides of the triangle are y=x,y=1 . x varies from 0 to 1 and y varies from x to 1.

First, compute the integral with respect to y.

D1x2+1dA=01[x11x2+1dy]dx=011x2+1[y]x1dx

Apply the limit value for y,

D1x2+1dA=011xx2+1dx=011x2+1dx01xx2+1dx=011x2+1dx12012xx2+1dx

Compute the integral with respect to x

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