In the adjacent figure the graph of two function `y=f(x)` and `y=sin x` are given y=sin x intersects, y=f(x) at A(a,f(a)),`B(pi,0) and C(2pi,0)`.
`A_(i)(i=1,2,3)` is the area bounded by the curves `y=f(x) and y=sin x` between x=0 and x=a,i=1 between x=a and `x=pi, i=2` between `x=pi` and `x=2pi,i=3`. If `A_(1)=1-sin a+(a-1)` cos a, determine the function f(x). Hence, determine a and `A_(1)`. Also, calculate `A_(2) and A_(3)`.
.

Answer

`A_(1)=1-sin 1, A_(2)=pi-1-sin 1, A_(3)=3pi-2`