Question

The line y = mx bisects the area enclosed by the lines x = 0, y = 0, x = 3/2 and the curve y = 1 + 4x – x2. Find the value of m.

Answer 1

Given curve is

y = 1 + 4x – x2

y = 5 – (x – 2)2

Now, the area OABO

Hence, the area OABCDO

According to the question,

9m/8 = (1/2) . (39/8)

m = 13/6

Hence, the value of m is 13/6.