1. Tardigrade
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  4. 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 L1 and L2 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.

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Q. 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.Mathematics Question Image

Application of Integrals

Solution:

$\therefore$ 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 $
$=6-4=2$

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