Y=0,5*x²-2x+3 y=7-x
0,5*x²-2x+3=7-x
0,5*x²-x-4=0 |×2
x²-2x-8=0 D=36 √D=6
x₁=-2 x₂=4 ⇒
₋₂∫⁴(7-x-(0,5x²-2x+3))dx=₋₂∫⁴(7-x-0,5x²+2x-3)dx=₋₂∫⁴(4+x-0,5x²)dx=
=(1/2)*₋₂∫⁴(8+2x-x²)dx=(1/2)*(8x+x²-x³/3) ₋₂|⁴=
=(1/2)(8*4+4²-4³/3-(8*(-2)+(-2)²-(-2)³/3))=(1/2)(32+16-64/3-(-16+4+8/3))=
=(1/2)(48-64/3-(-12+8/3))=(48-64/3+12-8/3)/2=(60-72/3)/2=(60-24)/2=36/2=18.
Ответ: S=18 кв.ед.