Discussion Forum



1)

The area under the curve y = |cos x - sin x|, 0≤x≤$\frac{\pi}{2}$


A) $2\sqrt{2}$

B) $2\sqrt{2}-2$

C) $2\sqrt{2}+2$

D) 0

Answer:

Option B

Explanation:

 y = |cos x - sin x|

2432021347_j2fj9ouro3qw-s.png

Required area = $2\int_{0}^{\frac{\pi}{4}} (\cos x -\sin x)dx$

$2 \left[\sin x+\cos x\right]_0^\frac{\pi}{4}$ = $2 \left[\frac{2}{\sqrt{2}}-1\right]$

$2\sqrt{2}-2$