First slide

Evaluation of definite integrals

Question

$\int_{0}^{10 π} [\tan^{- 1} x] d x =_________(w h e r e [] d e n o t e s G . I . F)$

Difficult

A

$π + \tan 1$
B

$10 π - \tan 1$
C

$10 π + \tan 1$
D

$10 π + 1$

Solution

$\int_{0}^{10 π} [\tan^{- 1} x] d x =$ $\int_{0}^{\tan 1} [\tan^{- 1} x] d x + \int_{\tan 1}^{10 π} [\tan^{- 1} x] d x$
= $\int_{0}^{\tan 1} 0 d x + \int_{\tan 1}^{10 π} 1 d x = 10 π - \tan 1$

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