Question

The area (in square units) of the region bounded by $x=-1,x=2,y=x^2+1$ and $y=2x-2$ is

• A. 10
• B. 7
• C. 8
• D. 9

Answer 1

Answer: (D)

9

$A_1=ar\left(ABC\right)$

$=\frac{1}{2}\times |2||4|$

$=4$ units

$A_2=ar\left(CDE\right)$

$=\frac{1}{2}\times 1\times 2$

$A_2=1$ units

Area of region between parabola and x-axis

$A_3={\int }_{-1}^2(x^2+1)dx={[\frac{x^3}{3}+x]}_{-1}^2$

Area required $=A_3+A_1-A_2$

$=6+4-1$

$=9$ units