diketahui f'(x) = 2x^2 + 5x - 2 dan f(1) = 19/6 maka f(x) adalah

anti turunan (integral)

F(x) = ∫ f ' (x)  dx

F(x) = ∫ (2x² + 5x - 2) dx
F(x)= 2/3 x³ + 5/2 x² - 2x + c
F(1) = 19/6
2/3 + 5/2- 2 + c = 19/6 ...ka;likan 6
4 + 15 -12 + 6c = 19
7 + 6c = 19
6c = 12
c= 2

f(x)= 2/3 x³ + 5/2 x² - 2x + 2

f (x) = integral (2x^2 + 5x - 2) dx
= 2/3 x^3 + 5/2 x^2 - 2x + c
maka,
f (1) = 2/3 1^3 + 5/2 1^2 - 2(1) + c
19/6 = (4+15-12)/6 + c
c = 19/6 - 7/6
c = 2

jadi, f(x) = 2/3 x^3 + 5/2 x^2 - 2x + 2