Find the area bounded by the curves y = -x² + 6x -5, y = -x² + 4x - 3 and the straight line y = 3x - 15.

$\frac{73}{6}$

The two parabolas can be re-written as and C₁:

(x - 3)² = -(y - 4) cut - axis at points noted (1, 0), (5, 0)

C₂ : (x - 2)² = -(y - 1) cut - axis at points noted (1, 0), (3, 0)

L: y = 3x -15 cut x-axis at points noted (5, 0)

(1, 0) is the common point of P₁ and P₂, (5, 0) is the common point of C₁ and L and C₂ and L meet at (4, -3).

Required area is : $\int\limits_1^4C_1dx-[\int\limits_1^4C_2dx+\int\limits_4^5l\,dx]$

Solve to get area = $\frac{73}{6}$