Let $f: R \rightarrow R$ defined by $f(x)=\cos x+x$ if $\int_\limits0^\pi f^{-1}(x) d x=\frac{\pi^2}{2}-k$, then the value of $k$ is ____.

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

Let

f: R \rightarrow R

defined by

f(x)=\cos x+x

\int\limits_{0}^\pi f^{-1}(x) d x=\frac{\pi^2}{2}-k

, then the value of

k

is ____.

View answer and explanation

Correct option: A

Option A (0) is correct because, after applying integration by parts and simplifying, the value of k is found to be 0.

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