Jika f'(x)=6x²+2 dan f(-1)=4, maka f(x)=?

f'(x) = 6x^2 + 2
f(x) = 2x^3 + 2x + C
f(-1) = 4
2(-1)^3 + 2(-1) + C = 4
2(-1) + 2(-1) + C = 4
-2 - 2 + C = 4
-4 + C = 4
C = 8

f(x) = 2x^3 + 2x + 8

integral

f(x)= ∫ f ' (x ) dx
f(x)= ∫ 6x²+ 2 dx
f(x)= 2x³ + 2x + c
f(-1) = 4 --> 2(-1)³ + 2(-1) + c = 4
-2 - 2 + c = 4
-4 + c = 4
c = 4+4
c = 8

f(x) = 2x³ + 2x + c --> c = 8
f(x)= 2x³ + 2x + 8