Diketahui F'(x)=6x^2-2x+3. Jika F(2)=12

Diketahui $F^{'} (x) = 6 x^{2} - 2 x + 3$ . Jika $F (2) = 12$ , $F (x) = \dots$

A. $2 x^{3} - x^{2} + 3 x - 7$

B. $2 x^{3} - 2 x^{2} + 3 x + 8$

C. $2 x^{3} - x^{2} + 3 x - 6$

D. $2 x^{3} - x^{2} + 3 x + 12$

E. $2 x^{3} - 2 x^{2} + 3 x - 15$

Diketahui:

$F^{'} (x) = 6 x^{2} - 2 x + 3$

$F (2) = 12$

Ditanya: $F (x)$

jawab

$F (x) = \int F^{'} (x) d x$

$F (x) = \int (6 x^{2} - 2 x + 3) d x$

$F (x) = \frac{6}{2 + 1} x^{2 + 1} - \frac{2}{1 + 1} x^{1 + 1} + 3 x + C$

$F (x) = \frac{6}{3} x^{3} - x^{2} + 3 x + C$

$F (x) = 2 x^{3} - x^{2} + 3 x + C$

mencari nilai C

$F (2) = 12$

$12 = 2 x^{3} - x^{2} + 3 x + C$

$12 = 2 (2)^{3} - (2)^{2} + 3 (2) + C$

$12 = 16 - 4 + 6 + C$

$12 = 18 + C$

$- 6 = C$

Kesimpulan

Jadi, $F (x) = 2 x^{3} - x^{2} + 3 x - 6$

Jawaban: C

  Muda Berkarya Intelektual Normatif

  Muda Berkarya Intelektual Normatif

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