Определим точки пересечения графиков :
x² - 4 = 5x + 2⇔ x² -5x -6 =0 ⇒ x₁ = -1 ; x₂ = 6 .
S = ∫ (5x+2 -(x² -4)) dx = ∫ (- x² + 5x + 6)dx =(-x³/3+5x²/2 +6x) | a =- 1 ; b=6
.......a = -1 ; b= 6 .........................................................................................
=(-6³/3 +5*6²/2+ 6*6 )-( (-1)³/3 +5*(-1)²/2 +6*(-1) ) =
-72+90+36 -( -1/3 +5/2 -6)= 54 -3 5/6 = 50 1/6 .