Question

Evaluate the integral without using a calculator:
[-1(bottom number),1(top number)] dx/(1+x^2)

Answer 1

why tan(u)?

Answer 2

I dont remember them... what are all the trigo. subs

Answer 3

\[\int\limits_{-1}^{1}\frac{ dx }{ 1+x^{2} }=tan^{-1}(b) - \tan^{-1}(a)\]
\[\ =tan^{-1}(1) - \tan^{-1}(-1) \]
\[\frac{ \pi }{ 4 }- \frac {-\pi}{ 4 } = \frac{ \pi }{ 4 }+\frac{ \pi }{ 4 } = \frac{2 \pi}{4}\]
\[=\frac{\pi}{2} \]