The value of ∫₁^(√3) (dx)/(1 + x²) is:

The value of $\int_1^{\sqrt{3}} \frac{dx}{1 + x^2}$ is:

(a)$\frac{\pi}{2}$
(b)$\frac{2\pi}{3}$
(c)$\frac{\pi}{6}$
(d)$\frac{\pi}{12}$

Answer

Correct option: (d)

Answer: (d) $\frac{\pi}{12}$ $\int_1^{\sqrt3}\frac{dx}{1+x^2} = \left[\tan^{-1}x\right]_1^{\sqrt3} = \frac{\pi}{3} - \frac{\pi}{4}$ Hence the value is $\frac{\pi}{12}$.