Question

Integrate
$\displaystyle \int^{ \: 1}_{0} \sf \small\frac{1}{1 + {x}^{2} } dx$
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Answer 1

Question:-

• Integrate $\displaystyle \int^{ \: 1}_{0} \sf \frac{1}{1 + {x}^{2} } dx$

Solution:-

$\displaystyle \int^{ \: 1}_{0} \sf \small \frac{1}{1 + {x}^{2} } dx$

$\sf = \bigg[ \tan^{ - 1}x \bigg]^{1} _{0}$

$\sf =[ \tan^{ - 1}(1) - { \tan}^{ - 1}(0)]$

$\sf = \frac{\pi}{4} - 0$

$\sf = \frac{\pi}{4}$

This is the required answer.

Answer 2

Solution is given in the above attachment..