A. -4 B. -3 C. -2 D. -1 E. 0
Nilai g(c/3) adalah –4.
Pembahasan
Integral Tentu
[tex]\begin{aligned}3x^2-6x+3&=\int_{c}^{x}g(t)\,dt\\&=\int_{c}^{x}\frac{d}{dt}\left(3t^2-6t+C\right)dt\\&=\Bigl[3t^2-6t\Bigr]_{c}^{x}\\3x^2-6x+3&=3x^2-6x-\left(3c^2-6c\right)\\\end{aligned}[/tex]
Memperhatikan kesamaan koefisien dan konstanta antara ruas kiri dan kanan, dapat diperoleh:
[tex]\begin{aligned}&-\left(3c^2-6c\right)=3\\&\Rightarrow 3c^2-6c=-3\\&\Rightarrow 3c^2-6c+3=0\\&\Rightarrow c^2-2c+1=0\\&\Rightarrow (c-1)^2=0\\&\therefore\ \boxed{\ c=\bf1\ }\end{aligned}[/tex]
Oleh karena itu:
[tex]\begin{aligned}&&g(t)&=\frac{d}{dt}\left(3t^2-6t+C\right)\\&\Rightarrow&g(t)&=6t-6\\&\Rightarrow&g\left(\frac{c}{3}\right)&=g\left(\frac{1}{3}\right)\\&&&=6\left(\frac{1}{3}\right)-6\\&&&=2-6\\&&&=\boxed{\ \bf{-}4\ }\end{aligned}[/tex]
KESIMPULAN
∴ Nilai g(c/3) adalah –4.
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