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Double integral problem

  • Thread starter Gwilim
  • Start date
  • #1
126
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Evaluate [tex] \int\ \int_R\ x^2e^ydA[/tex]

Over the rectangle R with vertices (0,0), (1,0), (1,3) and (0,3).

My answer:

[tex] \int\ \int_R\ x^2e^ydA = \int_0^3\ \int_0^1\ x^2e^ydA [/tex]
[tex] = \int_0^3\ [x^3/3]_0^1 e^y dy[/tex]
[tex] = 1/3 \int_0^3\ e^ydy [/tex]
[tex] = 1/3 (e^3-1) [/tex]

Double integrals are new to me, so if someome could check my answer that would be greatly helpful
 

Answers and Replies

  • #2
malawi_glenn
Science Advisor
Homework Helper
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looks ok.
 
  • #3
126
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seems too easy for 10 marks. There's barely three lines of working there.
 
  • #4
malawi_glenn
Science Advisor
Homework Helper
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seems too easy for 10 marks. There's barely three lines of working there.
well I dont know if 10marks is much or not. The integral is easy to solve since you had a rectangular area.
 
  • #5
126
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well I dont know if 10marks is much or not. The integral is easy to solve since you had a rectangular area.
The whole 2 hour paper has 100 marks in total. Anyway, thanks for the confirmation.
 
  • #6
63
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You are definitely correct. As for the facility with which you did this problem, you're just a superstar at this stuff ;)

Sometimes profs will toss in easy questions to discern who has, at least, a basic command of the principles involved from those who don't even know what an integrand is.
 
  • #7
1,752
1
Have confidence! GJ :)
 

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