Question

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

Answer 1

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

Answer 2

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

Answer 3

yep

Answer 4

We have to somehow use the tan function though

Answer 5

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

Answer 6

Any ideas?

Answer 7

We can also graph it for a hint

Answer 8

But we haven't learned integration by parts yet

Answer 9

@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...