Find the area bounded by the curves y = -x2 + 6x -5, y = -x2 + 4x - 3 and the straight line y = 3x - 15.
Answer & explanation
Correct answer: option 2
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 = $\frac{73}{6}$