   Chapter 15.2, Problem 21E

Chapter
Section
Textbook Problem

Evaluate the double integral.21. ∬ D ( 2 x − y ) d A , D is bounded by the circle with center the origin and radius 2

To determine

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

Explanation

Given

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

The domain D is bounded by the circle with radius 2 and the center is at origin.

Definition used:

Odd function: If f is a function and f(x)=f(x) , then f is said to be an odd function.

Formula used:

If f is an odd function, then aaf(x)dx=0 . (1)

Calculation:

The equation of the circle given is x2+y2=4 .

Therefore, y=±4x2 .

First, compute the integral with respect to y.

D(2xy)dA=22[4x24x2(2xy)dy]dx=22[2xyy22]4x24

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