CUET Preparation Today
The value of $\int\limits_0^{100}\left[\tan ^{-1} x\right] d x$, is |
100 100 - tan-1 1 100 - tan 1 none of these |
100 - tan 1 |
We have, $\int\limits_0^{100}\left[\tan ^{-1} x\right] d x =\int\limits_0^{\tan 1}\left[\tan ^{-1} x\right] d x+\int\limits_{\tan 1}^{100}\left[\tan ^{-1} x\right] d x$ $\Rightarrow \int\limits_0^{100}\left[\tan ^{-1} x\right] d x =\int\limits_0^{\tan 1} 0 d x+\int\limits_{\tan 1}^{100} 1 \cdot d x=100-\tan 1$ |
