Mathematics - Area Under Curves Question with Solution | TestHub

The graphs of $y=f(x)$ and $y=\sin x$ intersect at $P(a,f(a)),Q(\pi ,0)$ and $R(2\pi ,0)$, where $0<a<\pi$. The graph of $y=f(x)$ lies below that of $y=\sin x$ for $0<x<a$, above it for $a<x<\pi$, and below it for $\pi <x<2\pi$. Let $S_1,S_2,S_3$ be the areas bounded by the curves $y=f(x)$ and $y=\sin x$ between $x=0$ and $x=a$; between $x=a$ and $x=\pi$; and between $x=\pi$ and $x=2\pi$ respectively. It is given that $S=1-\sin t+(t-1)\cos t$ for all $t\le a$ represents the area bounded between $y=f(x)$ and $y=\sin x$ from $x=0$ to $x=t$.