Multiple choice

Evaluate: $\int^{\pi/4}_0 (1-\tan x)/(1+\tan x)dx $

  1. 0

  2. 1
  3. $ln2$
  4. $\dfrac{1}{2}ln2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\int^{\pi/4}_0 \dfrac{(1-\tan x)}{(1+\tan x)}dx = \int^{\pi/4}_0 \dfrac{(\cos x-\sin x)}{(\cos x+\sin x)}dx$ Let, cos x + sin x = t $\therefore$(- sinx + cos x) dx = dt

$\int^{\sqrt 2}_0 \dfrac{dt}{t}dx = [\log t] = \log \sqrt 2 = \dfrac{1}{2} \log 2$

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