f'(x) = (3x + 2)(x + 2) dan f(-1) = 5 ?

Materi Integral

f'(x) = 3x^2 + 8x + 4
f(x) = int (3x^2 + 8x + 4) dx
= x^3 + 4x^2 + 4x + C
f(-1) = 5 = (-1)^3 + 4(-1)^2 + 4(-1) + C
5 = -1 + 4 - 4 + C
C = 5 + 1 = 6.
Jadi,
f(x) = x^3 + 4x^2 + 4x + 6

F'(x) = (3x + 2)(x + 2) = 3x² + 8x + 4

F(x) = Int F'(x) dx
F(x) = Int (3x² + 8x + 4) dx
F(x) = x³ + 4x² + 4x + C

F(-1) = 5
-1 + 4 - 4 + C = 5
C = 6

Maka
F(x) = x³ + 4x² + 4x + 6