Question

Find the area under the curve y=arccosx between x=0 and x=1 and choose the right option

a:pi

b:cos pi/2

c:2 pi

d:sin pi/2

Answer 1

As $x=\cos y$, if $0<x<1$ then $0<y<\pi/2$ and the area under the curve is

$S=\int_{0}^{\pi/2}\cos ydy=\sin y|_0^{\pi/2}=\sin \pi/2$

The option (d)