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