Question

The area bounded by curve $y=x^2-1$ and tangents to it at $(2,3)$ and $y-$axis is

• A. $8/3$
• B. $2/3$
• C. $4/3$
• D. $1/3$

Answer 1

The correct option is B $2/3$

$x-axis:(-1,0)$

Area $={\int }_{-1}^0(x^2-1)dx$

$={[\frac{x^3}{3}-x]}_{-1}^0$

$=[\frac{-1}{3}-(-1\left)\right]-\left[0\right]$

$=-\frac{1}{3}+1$

$=\frac{2}{3}$ sq. units