Area of the region bounded by the curve $y=\cos x$ between $x=0, x=\pi$ and x-axis is:
Answer & explanation
Correct answer: option 2
y = cos x x = 0, x = π x axis
x = 0
from x = 0 to $\frac{\pi}{2}$ graphis pasitive ⇒ postitive area
from $x=\frac{\pi}{2}$ to $\pi$ graph is negative ⇒ negative area
so area = $\int\limits_0^{\frac{\pi}{2}} \cos x d x+\left(-\int\limits_{\frac{\pi}{2}}^\pi \cos x d x\right)$
-ve sign to counter -ve area
$=[\sin x]_0^{\frac{\pi}{2}}+[-\sin x]_{\frac{\pi}{2}}^\pi$
$1-0+[-0+1]$
$=1+1=2$
area = 2 sq. units