Question

Evaluate the given integral expression:

Answer 1

f(x) $\int\limits^ {} \, tanx dx$

log|sec x|

hence f(x) = log |sec x|

$\int\limits^\pi _\frac{\pi }{4}  {tanx} \, dx$ = f($\frac{\pi }{4}$) - f(0)

log| sec ($\frac{\pi }{4}$| - log |sec(0)|

log | $\sqrt{2}$ | - log| 1 |

log$\sqrt{2}$ - 0

log$\sqrt{2}$

log 2¹/₂

1/2 log 2 <==== answer