Question

\[\int\limits_1^\sqrt{3} \frac{1}{1 + x^2} dx\]  is equal to ______.

Options

• \[\frac{\pi}{12}\]
• \[\frac{\pi}{6}\]
• \[\frac{\pi}{4}\]
• \[\frac{\pi}{3}\]

• \[\frac{\pi}{2}\]

• \[\frac{2\pi}{3}\]

Answer 1

\[\int\limits_1^\sqrt{3} \frac{1}{1 + x^2} dx\]  is equal to `underlinebb(π/12)`.

Explanation:

Let I = `int_1^sqrt(3) dx/(1 + x^2)`

= `[tan^-1 x]_1^sqrt(3)`

= `tan^-1 sqrt(3) - tan^-1 1`

= `π/3 - π/4`

= `(4π - 3π)/12`

= `π/12`