Question

The following figure shows the graph of a continuous function $y=f(x)$ on the interval $[1,3]$. The points A, B, C have co-ordinates $(1,1),(3,2),(2,3)$ respectively and the lines $L_1$ and $L_2$ are parallel with $L_1$ being tangent to the curve at $C$. If the area under the graph of $y=f(x)$ from $x=1$ to $x=3$ is 4 square units, then find the area (in square units) of shaded region.

Answer 1

Answer: 0002

$\therefore$ Area of shaded region $=($ area of trapezium DEFG $)-($ area under $f(x))$
$=\frac{1}{2}\left(\frac{5}{2}+\frac{7}{2}\right)\times 2-4$
$=6-4=2$