Suppose i solved the integral (correctly) and i get as my answer $\displaystyle \arctan({\tan{x}})$ and i want the area from 0 to $\displaystyle \pi$...how do I solve that, what do i do to get around the 0-0??

thanks

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- Mar 29th 2009, 10:24 AMpolymerasesolving definate integrals
Suppose i solved the integral (correctly) and i get as my answer $\displaystyle \arctan({\tan{x}})$ and i want the area from 0 to $\displaystyle \pi$...how do I solve that, what do i do to get around the 0-0??

thanks - Mar 29th 2009, 10:41 AMSoroban
Hello, polymerase!

Note that: .$\displaystyle \arctan(\tan x) \:=\:x$

Also that: .$\displaystyle \arctan 0 \:=\:0,\:\pm\pi,\:\pm2\pi,\:\hdots$

What was the original integral?

It must have been equivalent to: .$\displaystyle \int 1\,dx$