Ответ:
4√3
Пошаговое объяснение:
y=y
1/2 x^2 +3x - 2 = - 1/2 x^2 - x -3
x^2 + 4x +1 =0
D = 4^2 - 4*1*1 = 12; √D = ±2√3
x = (-4 ±2√3) /2
x1 = -2 - √3 ; x2 = -2 + √3
∫ (- 1/2 x^2 - x -3 - ( 1/2 x^2 +3x - 2)) dx [x1;x2] =
= - ∫ (x^2 + 4x +1) dx [x1;x2] = - (x^3/3 + 2x^2 + x) [x1;x2] =
{ x1 = -2 - √3 ; x2 = -2 + √3 }
= - ((-2 + √3)^3/3 + 2(-2 + √3)^2 + (-2 + √3)) +
+ ((-2 - √3)^3/3 + 2(-2 - √3)^2 + (-2 - √3)) =
= 2√3 -10/3 + 10/3 + 2√3 = 4√3