Stuck on an integral

  • Thread starter BananaMan
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  • #1
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i have a double integral to reverse the order of and then integrate, i have reversed the order fine, however i am VERY stuck on the integration of the function in the first integral

integrate sin(y)/(x+y) dx between 0 and y

any pointers greately appreciated
 

Answers and Replies

  • #2
Galileo
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You're integrating wrt x, right? So sin(y) is a contant as far as the integration is concerned.
 
  • #3
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so it would just be sin(y) * integral 1/(x+y)

therefore sin(y) * ln(x+y)

if so im going to feel like a fool :P
 
  • #4
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if this is the case i have now integrated it and subbed for (y) (from the limits) to get sin(y)*ln(2y) but i must now integrate that function wrt y, which is even harder than the first function >.< and i am very stuck, maybe integration by parts here?
 
  • #5
benorin
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Don't feel like a fool; the thing is so. Post the bounds so we can help...
 
  • #6
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ok the original integral was between y and 0 hence getting sin(y)*ln(2y)

now the integral is that function ive just typed between pi/2 and 0 dy

im muchos stuck
 
  • #7
dextercioby
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[tex] -\int_{0}^{\frac{\pi}{2}} \sin y \ \ln 2y \ dy =-\left[ \mbox{Ci}\left( \frac{1}{2}\pi \right) +\ln 2-\gamma\right][/tex].

Daniel.
 
  • #8
Galileo
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The bounds on the first integral are y and 0 right? So just enter the bounds correctly. Don't skip too many steps or you might miss a simplification:
[tex]\ln(x+y)|^{x=y}_{x=0}=\ln(2y)-\ln(y)=\ln(\frac{2y}{y})=\ln2[/tex]

Which doesn't even depend on y, so the integral is easy as pie.
 
  • #9
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Galileo said:
The bounds on the first integral are y and 0 right? So just enter the bounds correctly. Don't skip too many steps or you might miss a simplification:
[tex]\ln(x+y)|^{x=y}_{x=0}=\ln(2y)-\ln(y)=\ln(\frac{2y}{y})=\ln2[/tex]

Which doesn't even depend on y, so the integral is easy as pie.

thanks :)

i just forgot to seperate the variables and made life hard on myself
 

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