Misalkan f’(x) turunan dari f(x). jika f’(x) = 6x^2 - 4x + 1 dan f(2) = 4, fungsi f(x) = … Terima kasih

f(x)= ∫ f' (x) dx


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

diketahui [tex]f'\left(x\right)=6x^{2}-4x+1[/tex] dan [tex]f(2)=4[/tex], [tex]f(x)=?[/tex]

Selanjutnya integralkan

[tex]\begin{align*} \int f'\left(x\right)dx & =\int\left(6x^{2}-4x+1\right)dx\\ f\left(x\right) & =2x^{3}-2x^{2}+x+C \end{align*}[/tex]

karena [tex]f(2)=4[/tex] maka

[tex]\begin{align*} 4 & =2\left(2^{3}\right)-2\left(2^{2}\right)+2+C\\ 4 & =16-8+2+C\\ 4 & =10+C\\ -6 & =C \end{align*}[/tex]

sehingga [tex]f\left(x\right)=2x^{3}-2x^{2}+x-6[/tex]