Double integration problem

  • Thread starter Enzo
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  • #1
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Homework Statement



[tex]
\int^1_y\int^1_0 x^2*e^{xy} dydx
[/tex]


Answer: [tex]1/2 (e-2)[/tex]

The Attempt at a Solution



I've tried about 4 ways of doing this, I can't solve it. It either ends up being a completely huge and wrong answer, or ends up giving me a integration by parts of something like [tex]\int e^(x^2) dx[/tex] which I cant solve
 
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Answers and Replies

  • #2
tiny-tim
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Hi Enzo! :smile:

(have an integral: ∫ and try using the X2 tag just above the Reply box :wink:)
[tex]
\int^1_y\int^1_0 x^2*e^{xy} dydx
[/tex]


Answer: [tex]1/2 (e-2)[/tex]

… ends up … something like [tex]\int e^(x^2) dx[/tex] which I cant solve
Did you change the order of integration first?

I get ∫xex2 dx, which is easy :wink:

Try again! :smile:
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,833
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Homework Statement



[tex]
\int^1_y\int^1_0 x^2*e^{xy} dydx
[/tex]


Answer: [tex]1/2 (e-2)[/tex]

The Attempt at a Solution



I've tried about 4 ways of doing this, I can't solve it. It either ends up being a completely huge and wrong answer, or ends up giving me a integration by parts of something like [tex]\int e^(x^2) dx[/tex] which I cant solve
This makes no sense. The way you have it written, with the "outer integral" from y to 1, the answer must be a function of y, not a constant. But, as written it does not give "[itex]e^{x^2}[/itex]
[tex]\int_{x=y}^1\int_{y= 0}^1 x^2e^{xy}dy dx= \int_{x=y}^1\left(xe^{xy}\right)_0^1 dx[/tex]
[tex]= \int_{x=y}^1 \left(xe^x- x\right)dx[/tex]
which can be done by a single integration by parts.

If it were
[tex]\int_{y=0}^1\int{x=y}^1 x^2e^{xy}dx dy[/itex]
tat can be done by two integrations by parts.
 

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