Diketahui f'(x)=6x^2-2x+1 dan f(2) = 4. Tentukan f(x).

f(x) = integral f'(x)
f(x) = 2x^3 - x^2 + x + C
f(2) = 2(2^3) - 2^2 + 2 + C
4 = 16 - 4 + 2 + C
4 = 14 + C
C = 14 - 4
C = 10

f(x) = 2x^3 - x^2 + x + 10

Bab Integral
Matematika SMA Kelas XI

f'(x) = 6x² - 2x + 1

∫ (6x² - 2x + 1) dx
=6/(2 + 1) x²⁺¹ - 2/(1 + 1) . x¹⁺¹ + 1x
= 2x³ - x² + x + C

f(2) = 2 . 2³ - 2² + 2 + C = 4
C = 4 - 14
C = - 10

f(x) = 2x³ - x² + x - 10