Question

If the area of the region bounded by point (x, y) satisfying the condition $\left\{\right(x,y);0\le y\le x^2+1,0\le y\le x+1,x=0,x=2,y=0\}isA(unit{)}^{2}then\left[\frac{23}{A}\right]equalsto$

Answer 1

Considering the curve $y=x^2+1$ and the lines
$y=x+1$
$y=0$
$x=0$
and $x=2$
according to Question the required region is the shaded region
$RequiredArea=\stackrel{1}{\underset{0}{\int }}(x^2+1)dx+areaofBMNC$
$A=\frac{1}{3}+1+\frac{1}{2}(2+3).1=\frac{23}{6}\Rightarrow \left[\frac{23}{A}\right]=6$