Question

Evaluate : $\int\limits^{\pi/4}_0 {\frac{1}{1+x^{2}}} \, dx$

Answer 1

Solution:

As we know that

$\int {\frac{1}{1+x^{2}}} \, dx = {tan}^{ - 1} x + c$
So here

$\int\limits^{\pi/4}_0 {\frac{1}{1+x^{2}}} \, dx = ( {tan}^{ - 1} x)0 \: \: \: to \: \: \frac{\pi}{4}$
now put upper then lower limit

$( {tan}^{ - 1} \frac{\pi}{4} ) - ( {tan}^{ - 1} 0) \\ \\ = ( {tan}^{ - 1} x)$