Double int reversing

  • Thread starter kieranl
  • Start date
  • #1
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Homework Statement



sketch the region of integration and write an equivalent integral with order of integration reversed. Then evaluate both integrals to confirm their equality

Homework Equations



[tex]\int\int[/tex]dydx for 0<=x<=1 and 0<=y<=[tex]\sqrt{x}[/tex]

The Attempt at a Solution



i rearanged the limits so the equation becomes
[tex]\int\int[/tex]dxdy for 0<=x<=y2 and 0<=y<=1

but my calculations for the first equation came to 2/3 and the second equation came to 1/3

plus the answer is 1/6 so im obviously doing something wrong. can someone help? have i even written the second equation right?
 

Answers and Replies

  • #2
590
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Did you first sketch the region of integration? The limits for the second integral(with order of integration reversed) should be taken such that you still integrate over the same region. Do you know how to do this?
 
  • #3
24
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yeh im pretty sure i drew it properly??
 

Attachments

  • region.bmp
    190 KB · Views: 373
  • #4
590
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Since your attachment is pending approval, assuming your diagram is correct, think about the new set of limits you have to use when you change the order of integration. How do x and y vary now?
 

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