Find the area of a region bounded by y= 2x-x^2, y= 2x-4

Question

I'm trying to find the area bounded by those given curves and I need help.

Answer 1

1....y=-x^2+2x...parabola that tern down

2....y=2x-4...strate line with slope=2 & go thru (0,-4)

Tu get hit points...-x^2+2x=2x-4...-x^2=-4 or x^2=+4...so x=+-2

so integrate from x=-2 tu x=+2 the 2 kervs

strate line go from (-2,-8) tu (+2,0)...triangel, so area=(1/2)4*8)=4*4=16

But all av that be belo x-axis

Tu get top line, integrate y=-x^2+2x...-(2/3)x^3+x^2

Kerved pees kerv up tu (1,1)...the top, then down tu (2,0)

Wen me integrate the parabola, me get its area=0

Area tween 2 kervs=top area -bottom area...0-(-16)=+16