Question

a curve is governed by the equation Y = cos x then what is the area enclosed by the curve and x-axis between x =o and x = π/2 is shaded region

Answer 1

integration of cosx from limit 0-pie/2
since integration of cosx is sinx
substitution of limit
sin pie/2 -sin0
1-0=1

Answer 2

Answer: 1 square units


The given curve is $y=\cos x$


We have to find the area enclosed by the curve between two points. In mathematical terms, we are asked to find integral of $y=\cos x$ between the two points.



So, if Area is $A$, then

$A = \displaystyle \int\limits_{0}^{\frac{\pi}{2}} \cos x \, \, dx \\ \\ \\ \implies A = \left[ \sin x \right]_{0}^{\frac{\pi}{2}} \\ \\ \\ \implies A = \sin \frac{\pi}{2} - \sin 0 \\ \\ \\ \implies A = 1-0 \\ \\ \\ \implies \boxed{\bold{A=1}}$


Thus, The area enclosed by $\bold{y=cos \, x}$ between $\bold{0}$ and $\bold{\frac{\pi}{2}}$ is 1.