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baddinlol Group Title

Area under y = arctan(x) between x = 1 and x = 0

  • 2 years ago
  • 2 years ago

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  1. baddinlol Group Title
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    I don't understand how to integrate arctan(x) by hand

    • 2 years ago
  2. lgbasallote Group Title
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    i think i remember it having something to do with integration by parts...

    • 2 years ago
  3. mukushla Group Title
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    yep

    • 2 years ago
  4. baddinlol Group Title
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    We have to somehow use the tan function though

    • 2 years ago
  5. baddinlol Group Title
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    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

    • 2 years ago
  6. baddinlol Group Title
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    Any ideas?

    • 2 years ago
  7. baddinlol Group Title
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    We can also graph it for a hint

    • 2 years ago
  8. baddinlol Group Title
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    But we haven't learned integration by parts yet

    • 2 years ago
  9. .Sam. Group Title
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    @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...

    • 2 years ago
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