^3_11 1+x^2 dx is equal to: 1. 12 2. 6 3. 4 4. 3 - Vidyadip

Question

$\int\limits^\sqrt{3}_1\frac{1}{1+\text{x}^2}\text{ dx}$ is equal to:

$\frac{\pi}{12}$
$\frac{\pi}{6}$
$\frac{\pi}{4}$
$\frac{\pi}{3}$

✓

Answer

$\frac{\pi}{12}$

Solution:

$\int\limits^\sqrt{3}_1\frac{1}{1+\text{x}^2}\text{dx}$

$=\big[\tan^{-1}\text{x}\big]^\sqrt{3}_1$

$=\frac{\pi}{3}-\frac{\pi}{4}$

$=\frac{\pi}{12}$

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