Question

Area bounded by the curves $y=[\frac{x^2}{64}+2]$ ([.] denotes the greatest integer function ) $y=x-1$ and $x=0$ above the $x-axis$ is

• A. $2$
• B. $3$
• C. $4$
• D. none of these

Answer 1

Answer: (C)

$4$

Only when $x>8$ step value of given function is greater than 2

$\Rightarrow$when $0<x<8$, step value of given function is slightly greater than 2 $\Rightarrow$step value =2 in $0<x<8$

We can see in above figure, common area is ABCD(trapezium)

$\Rightarrow$common area =area of rectangle ABED+area of triangle BEC

$\Rightarrow$Common area =$(2\times 1)+\frac{1}{2}\times 2\times 2$

$\Rightarrow$Common area =4