Question

Evaluate the integral
${\int }_0^1\frac{1}{1+x^2}dx$

• A. $\pi /4$
• B. $\pi$
• C. $\pi /3$
• D. $0$

Answer 1

The correct option is A $\pi /4$

${\int }_0^1\frac{1}{1+x^2}dx$

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

${\int }_0^1\frac{1}{1+x^2}dx={\tan }^{-1}x+c{|}_0^1$

$=\left({\tan }^{-1}\right(1)+c)-\left({\tan }^{-1}\right(0)+c)$

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