anonymous
  • anonymous
Area under y = arctan(x) between x = 1 and x = 0
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
I don't understand how to integrate arctan(x) by hand
lgbasallote
  • lgbasallote
i think i remember it having something to do with integration by parts...
anonymous
  • anonymous
yep

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anonymous
  • anonymous
We have to somehow use the tan function though
anonymous
  • anonymous
It says use the fact that y=artan(x) is the inverse of y = tan(x) to calculate the area between x = 1 and x =0
anonymous
  • anonymous
Any ideas?
anonymous
  • anonymous
We can also graph it for a hint
anonymous
  • anonymous
But we haven't learned integration by parts yet
.Sam.
  • .Sam.
@baddinlol You have to use integration by parts here, \[\int\limits \tan ^{-1}(x) \, dx\] \[u=\tan^{-1}x~~~~~dv=dx \\ \\ du=\frac{1}{1+x^2} ~~~~~v=x\] \[x \tan ^{-1}x-\int\limits \frac{x}{1+x^2} \, dx\] Then continue...

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