In the picture above, line y = c intersects with parabola y = 6x-x^2 in the first quadrant.
If the gray area below line y = c and the gray area above line y=c are equal, then value of c is ...
Area under parabola = 2/3* base * height
Area above parabola = 1/3 * base* height
Area = definite integral
The Attempt at a Solution
Parabola y=6x-x^2 has peak point (3,9)
Suppose a is the x-intercept of the line and parabola.
At x = a, c equals 6a-a^2
So, the gray area below the line is 1/3 * a * (6a-a^2)
The base for the upper gray parabola area is 2(3) - 2a = 6-2a
So, the gray area above the line is 2/3 * (6-2a) * (9-(6a-a^2))
I get a = 1.592
and c = 6a-a^2 = 7.017
However, I'm sure the correct answer is 27/4 (I've tested it using integral method)