Question

The area bounded by the curve $y=\left\{x\right\}$ with the $x$ -axis from $x=\pi $ to $x=3.8$ is $\left(\frac{\pi }{2} - a\right)\left(b - \pi \right)$ sq. units, then the value of $b-a$ is equal to (where $\left\{.\right\}$ denotes the fractional part function)

Answer 1

Required Area $=$ Area of Trapezium
$=\frac{1}{2}$ (Sum of parallel sides) (Distance between them)
$=\frac{1}{2}\left(\left\{\pi \right\} + \left\{3.8\right\}\right)\left(3.8 - \pi \right)$
$=\frac{1}{2}\left(\pi - 3 + 0.8\right)\left(3.8 - \pi \right)$
$=\frac{1}{2}\left(\pi - 2.2\right)\left(3.8 - \pi \right)$
$=\left(\frac{\pi }{2} - 1.1\right)\left(3.8 - \pi \right)$ sq. units
$\Rightarrow b=3.8, \, a=1.1$