First slide

Evaluation of definite integrals

Question

$\int_{0}^{102} [\tan^{- 1} x] d x = Where [.] = G I F$

Moderate

A

$102 - \tan 1$
B

101
C

$102 + \tan 1$
D

$102 - \frac{π}{4}$

Solution

$\begin{array}{l} For 0 \leq x \leq \tan 1 and \tan 1 \leq x \leq 102 \\ \int_{0}^{102} [\tan^{- 1} x] d x = \int_{0}^{\tan 1} 0 d x + \int_{\tan 1}^{102} 1 d x = (x)_{\tan 1}^{102} = 102 - \tan 1 \end{array}$

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