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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Use geometry or symmetry, or both, to evaluate the double integral.

65. D ( x + 2 ) d A ,

D = { ( x , y ) | 0 y 9 x 2 }

To determine

To calculate: The value of given double integral over D using symmetry or geometry or both.

Explanation

Given

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

The domain is, D={(x,y)|0y9x2} .

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)

Thus, D1dA=A(D) (2)

Calculation:

The value of the given double integral is,

D(x+2)dA=DxdA+D2dA=3309x2xdydx+3309x22dydx

From (1), first term will become 0

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Chapter 15 Solutions

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