Question

Find the area bounded by the y-axis, the line y = 1, and the arc of y = sin x between x = 0 and x = 𝜋/2.

Answer 1

$S=\int_0^{\frac{\pi}{2}}(1-sinx)dx=(x+cosx))|_0^{\frac{\pi}{2}}=\\ =\frac{\pi}{2}+cos\frac{\pi}{2}-cos0=\frac{\pi}{2}-1$