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∫1311+x2dx is equal to ______. - Mathematics

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Question

\[\int\limits_1^\sqrt{3} \frac{1}{1 + x^2} dx\] is equal to ______.

Options

\[\frac{\pi}{12}\]
\[\frac{\pi}{6}\]
\[\frac{\pi}{4}\]
\[\frac{\pi}{3}\]
\[\frac{\pi}{2}\]
\[\frac{2\pi}{3}\]

MCQ

Fill in the Blanks

Solution

\[\int\limits_1^\sqrt{3} \frac{1}{1 + x^2} dx\] is equal to `underlinebb(π/12)`.

Explanation:

Let I = `int_1^sqrt(3) dx/(1 + x^2)`

= `[tan^-1 x]_1^sqrt(3)`

= `tan^-1 sqrt(3) - tan^-1 1`

= `π/3 - π/4`

= `(4π - 3π)/12`

= `π/12`

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Definite Integrals

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Chapter 20: Definite Integrals - MCQ [Page 118]

APPEARS IN

RD Sharma Mathematics [English] Class 12

Chapter 20 Definite Integrals
MCQ | Q 15 | Page 118

2023-2024 (February) Official (with solutions)

Q 1.vi | 1 mark

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