   Chapter 15.2, Problem 18E

Chapter
Section
Textbook Problem

Evaluate the double integral.18. ∬ D ( x 2 + 2 y )   d A , D is bounded by y = x, y = x3, x ≥ 0

To determine

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

Explanation

Given

The function is f(x,y)=(x2+2y) .

The domain D is bounded by y=x,y=x3,x0 .

Calculation:

First, compute the integral with respect to y.

D(x2+2y)dA=01[x3x(x2+2y)dy]dx=01[x2y+2y22]x3xdx=01[x2y+y2]x3xdx

Apply the limit value for y,

DxcosydA=01[(x2x</

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