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Chapter 5: Q31P (page 248)

∫x=0ln16∫y=ex/24dydxlny

Short Answer

Expert verified

The required solution is 6.

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∫∫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:1→4,andx:0→2lny

So, the integration

l=∫14dylny∫02lnydx=∫14dylny2lny=2∫14dy=6

Therefore, the value of the integration is, 6.

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Most popular questions from this chapter

∫Kdr1-K2r2=sin-1Kror-cos-1Krortan-1Kr1-K2r2

Hints: Sketch a right triangle with acute angles u and v and label the sides so that sinu=Kr. Also, note thatu+v=ττ/2; then if u is an indefinite integral, so is -v since they differ by a constant of integration.

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∫∫ydxdyover the triangle with vertices (-1,0),(0,2),and(2,0)

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See all solutions

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