The value of $\int\limits_0^{100}\left[\tan ^{-1} x\right] d x$, is
Answer & explanation
Correct answer: option 3
We have,
$\int\limits_0^{100}\left[\tan ^{-1} x\right] d x =\int\limits_0^{\tan 1}\left[\tan ^{-1} x\right] d x+\int\limits_{\tan 1}^{100}\left[\tan ^{-1} x\right] d x$
$\Rightarrow \int\limits_0^{100}\left[\tan ^{-1} x\right] d x =\int\limits_0^{\tan 1} 0 d x+\int\limits_{\tan 1}^{100} 1 \cdot d x=100-\tan 1$