Diketahui $F'(x)=6x^2-2x+3$. Jika $F(2)=12$, $F(x)=\dots$
A. $2x^3-x^2+3x-7$
B. $2x^3-2x^2+3x+8$
C. $2x^3-x^2+3x-6$
D. $2x^3-x^2+3x+12$
E. $2x^3-2x^2+3x-15$
Diketahui:
$F'(x)=6x^2-2x+3$
$F(2)=12 $
Ditanya:$F(x)$
jawab
$F(x)=\int F'(x) dx$
$F(x)=\int (6x^2-2x+3)dx $
$F(x)= \frac{6}{2+1}x^{2+1}-\frac{2}{1+1}x^{1+1}+3x+C $
$F(x)=\frac{6}{3}x^3-x^2+3x+C$
$F(x)=2x^3-x^2+3x+C $
mencari nilai C
$F(2)=12$
$12=2x^3-x^2+3x+C $
$12=2(2)^3-(2)^2+3(2)+C$
$12= 16-4+6+C$
$12=18+C$
$-6=C$
Kesimpulan
Jadi, $F(x)=2x^3-x^2+3x-6$
Jawaban: C
Muda Berkarya Intelektual Normatif