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Chapter 5: Q30P (page 248)

鈭�x=02鈭�y=x2e-y2/2dydx

Short Answer

Expert verified

The required solution is1-e-2

Step by step solution

01

Definition of double integral

The double integral of f(x,y)over the area Ain the (x,y)plane as the limit of this sum, and we write it as

鈭�鈭�Af(x,y)dxdy

02

Drawing the area bounded by the curve

The area of integration or bounded region is shown below,

03

Calculation of the area under the curve changing boundaries

Changing the boundaries of the given integration:

y:0鈫�2,andx:0鈫�y

So, the integration

l=鈭�02e-y2/2dy鈭�0ydx=鈭�02e-y2/2ydy=鈭�02e-y2/2d-y2/2=e-y2/202=-e-2-1=1-e-2

Therefore, the value of the integration is,1-e-2

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Most popular questions from this chapter

Let the solid in Problem 7 have density =cos胃.

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鈭�x=04鈭�y=0xxydydx

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