find the area of the region bounded by the graphs of y=-x^2+5x+2 and y=2

Answer 1

The graphs intersect at (0,2) and (5,2). So, the area is just the region below the parabola and above the line:

a = ∫[0,5] y-2 dx
= ∫[0,5] (-x^2+5x+2-2) dx = 125/6

Answer 2

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