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baddinlol 2 years ago Area under y = arctan(x) between x = 1 and x = 0

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1. baddinlol

I don't understand how to integrate arctan(x) by hand

2. lgbasallote

i think i remember it having something to do with integration by parts...

3. mukushla

yep

4. baddinlol

We have to somehow use the tan function though

5. baddinlol

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

6. baddinlol

Any ideas?

7. baddinlol

We can also graph it for a hint

8. baddinlol

But we haven't learned integration by parts yet

9. .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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