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INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS1 Mark
Question
$\int\limits^\sqrt{3}_1\frac{1}{1+\text{x}^2}\text{ dx}$ is equal to:
  1. $\frac{\pi}{12}$
  2. $\frac{\pi}{6}$
  3. $\frac{\pi}{4}$
  4. $\frac{\pi}{3}$
✓

Answer

  1. $\frac{\pi}{12}$

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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