Using multivariable Calculus

Question

Find two numbers x and y (x ≤ y) such that y∫x (6-t-t²dt) is as largest as possible

Answer 1

6-t-t² is a parabola and this expression is -(t+3)(t-2), so the parabola is an inverted U shape, intersecting the x-axis at -3 and 2.

The integral is the area between the curve and the x-axis. This area is maximum between the x-intercepts, so x=-3 and y=2.