   Chapter 15.2, Problem 19E

Chapter
Section
Textbook Problem

Evaluate the double integral.19. ∬ D y 2   d A , D is the triangular region with vertices (0, 1), (1, 2), (4, 1)

To determine

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

Explanation

Given

The function is f(x,y)=y2 .

The domain D is triangular region with vertices (0,1),(1,2),(4,1) .

Calculation:

The equation of the sides of the triangle are x=y1 , y=1 , and x=73y .

First, compute the integral with respect to x.

Dy2dA=12[y173yy2dx]dy=12[y2x]y173ydy

Apply the limit value for x,

Dy2dA=12[y2(73y)y2(y1)]dy=12

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