^3_11 1+x^2 dx is equal to: - Vidyadip

MCQ

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

✓
$\frac{\pi}{12}$
B
$\frac{\pi}{6}$
C
$\frac{\pi}{4}$
D
$\frac{\pi}{3}$

✓

Answer

Correct option: A.

$\frac{\pi}{12}$

$\int\limits^\sqrt{3}_1\frac{1}{1+\text{x}^2}\text{dx}$
$=\big[\tan^{-1}\text{x}\big]^\sqrt{3}_1$
$=\frac{\pi}{3}-\frac{\pi}{4}$
$=\frac{\pi}{12}$

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