f'(x) = (x-2)(x+4) dan f(-2) = 3, Tentukan f(x)

f'(x) = x^2 + 2x - 8

f(x) = integral f'(x) dx
f(x) = integral (x^2 + 2x - 8) dx
f(x) = 1/3 x^3 + x^2 - 8x + C

substitusi f(-2) = 3

1/3 (-2)^3 + (-2)^2 - 8(-2) + C = 3
-8/3 + 4 + 16 + C = 3
-8/3 + 20 + C = 3
C = 3 + 8/3 - 20
C = 9/3 + 8/3 - 60/3
C = (9+8-60)/3
C = -43/3

jadi
f(x) = 1/3x^3 + x^2 - 8x - 43/3

Mapel : Matematika
Kelas : XI SMA
Bab : Turunan

Pembahasan :
F'(x) = x² + 2x - 8
F(x) = 1/3x^3 + x² - 8x + C

F(-2) = -8/3 + 4 + 16 + C
3 + 8/3 = 20 + C
17/3 = 20 + C
C = 17/3 - 20
C = -43/3

F(x) = 1/3x^3 + x² - 8x - 43/3