Question

Evaluate the definite integrals: $\int^\frac{\pi}{4}_0 {tan\ x} \, dx$

Answer 1

Answer:

$log\sqrt{2}$

Step-by-step explanation:

Concept:

$\int{tanx}\:dx=log\:secx+c$

Now,

$\int\limits^{\frac{\pi}{4}}_0{tanx}\:dx\\\\=[log\:secx]^\frac{\pi}{4}}_0\\\\=log\:sec(\frac{\pi}{4})-log\:sec(0)\\\\=log\sqrt{2}-log1\\\\=log\sqrt{2}-0\\\\=log\sqrt{2}$