₁^{{3}} dx/1+x² equals - NCERT Class XII Mathematics Chapter

NCERT Class XII Mathematics Chapter - - Solutions

Choose the correct answer in Exercises 196 and 197.

Question : 196 of 271

Marks: +1, -0

\int\limits_{1}^{\sqrt{3}} \frac{dx}{1+x^2}

equals

Solution:

Let

I = \int\limits_{1}^{\sqrt{3}} \frac{dx}{1+x^2}

= [\tan^{-1}x]_{1}^{\sqrt{3}}

= \tan^{-1}\sqrt{3} - \tan^{-1}1

= \frac{\pi}{3} - \frac{\pi}{4} = \frac{\pi}{12}

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