## anonymous 3 years ago Area under y = arctan(x) between x = 1 and x = 0

1. anonymous

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

2. anonymous

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

3. anonymous

yep

4. anonymous

We have to somehow use the tan function though

5. 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

6. anonymous

Any ideas?

7. anonymous

We can also graph it for a hint

8. anonymous

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...