Set up, but do not evalute, to find the area of the region bounded by the graphs of y=10x-x^2, y=2x and x=10. Sketch the graph

Answer 1

I would do the sketch first.
A simple quick solution will show that the parabola cuts the line at
(0,) and (8,16) , so you have a nice inclosed region form (0,0) to (8,16) where
the parabola is above the straight line, and another region from
x = 8 to x = 10 with the straight line above the parabola

so area
= ∫ (10x - x^2 - 2x) dx from 0 to 8 + ∫ (2x - 10x + x^2) dx from 8 to 10

there is your setup, now your turn.