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Double integral - reversing order

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



[tex]
\displaystyle\int^1_0 \int^{e^x}_{1}dydx
[/tex]

Homework Equations


none


The Attempt at a Solution


the above integral i can do with no problem, but changing the order of integration give me a totally different answer and need to know if i am doing it correct

First off
[tex]
\displaystyle\int^1_0 \int^{e^x}_{1}dydx = e^1 - 2
[/tex]

To reverse the order of integration i get:
[tex]
\displaystyle\int^{e^1}_1 \int^{ln(y)}_{0}dxdy
[/tex]
which gives me 1 which is wrong

Before i post how i went about my solution I want to know if i am doing my limit right?
 
Last edited:

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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Did you draw a graph of the integration region? x doesn't go from 0 to ln(y).
 
  • #3
44
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it goes from 0 to ln(e^1) which is 0 to 1

considering y=e^x then x = ln(y)

but im guessing my understanding is wrong
 
Last edited:
  • #4
44
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Ok, these are two questions alike. Can you please tell me if i am completely misunderstanding the region of integration.
I need to show by reversing the order that i still get the same answer.

[URL]http://www.users.on.net/~rdenker/assign1.jpg[/URL]

EDIT: ok, another quick question. For Question 4 in the image here, is my region of integration on the wrong side of the line???
 
Last edited by a moderator:
  • #5
Dick
Science Advisor
Homework Helper
26,258
618
Your graph is on the correct side of the line. But look at it and imagine integrating dx. Isn't ln(y) the LOWER bound for x?
 
  • #6
44
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that seemed so hard to wrap my head around at the time but is so simple now
thanks!
 

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