Optimization or area under parabola
This question isn't really optimization but the second part is (which I know how to do). Its the first part i'm stuck at.
The cross-section of a building constructed inside a parabolic framework is shown in the diagram.
(sorry for bad drawing)
a) Given that PQ is 2xm show that the shaded area is 6x - 2x^3
The only thing I can think of is to multiply the equation of the parabola
(3 - x^2) by 2x, which gives 6x - 2x^3 .
Can you tell how the proper way to do it is?