Question

The area under the curve y=cos²x between x=0 and x=π is.....,Select correct option from the given options.
(a) π
(b) π/2
(c) 2π
(d) 2

Answer 1

The area under the curve $y=\cos^2x$ from $x=0$ to $x=pi$ is given as

$\int_0^{\pi}\cos^2xdx$

$=2\int_0^{\pi/2}\cos^2xdx$

$=2\int_0^{\pi/2}\left(\frac{1+\cos2x}{2}\right)dx$

$=\left(x+\frac{\sin2x}{2}\right)_0^{\pi/2}$

$=\pi/2$

Hence, option (b)  is correct answer