Find the exact area below the curve y=x^5(3−x) and above the x-axis.

Answer 1

the curve lies above the x-axis on the interval [0,3].
So, the area is

∫[0,3] x^5(3-x) dx = ∫[0,3] 3x^5 - x^6 dx = 1/2 x^6 - 6x^5[0,3] = 729/14