Question

The area (in sq. units) bounded by the parabola $y=x^2-1$ , the tangent at the point (2,3) to it and the y-axis is:

• A. $\frac{14}{3}$
• B. $\frac{56}{3}$
• C. $\frac{8}{3}$
• D. $\frac{32}{3}$

Answer 1

Answer: (A)

$\frac{14}{3}$

Equation of tangent at $(2,3)$ on
$y=x^2-1$, is $y=(4x-5).......\left(i\right)$
$\therefore$ Required shaded area
$=ar\left(△ABC\right)-\underset{-1}{\overset{3}{\int }}\sqrt{y+1}dy$
$=\frac{1}{2}.\left(8\right).\left(2\right)-\frac{2}{3}\left(\right(y+1{)}^{3/2}{)}_{-1}^3$
$=8-\frac{16}{3}=\frac{8}{3}$