JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Hard

1 of 1

Application +4 | -1

The value of

\int\limits_{{-1}}^1 \frac{d}{d x}\left(\tan ^{-1} \frac{1}{x}\right) d x

, is

View answer and explanation

Correct option: C

-\pi / 2

Option C (-

\frac{\pi}{2}

) is correct because the derivative of

\tan^{-1}(\frac{1}{x})

is -

\frac{1}{1+x^2}

, and integrating this from -1 to 1 gives -

\frac{\pi}{2}

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