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

Step-by-step solution

We have, d y d x = 2 x ∴ Slope of tangent at 2 , 3 is m = 4 ∴ Equation of tangent is y - 3 = 4 x - 2 ∴ Point T ≡ 0 , - 5 ∴ Area of Δ P T M = 1 2 × 8 × 2 = 8 Area of curve P A M P = ∫ - 1 3 y + 1 d y = 2 3 y + 1 3 2 - 1 3 = 16 3 ∴ Required shaded area = 8 - 16 3 = 8 3