Diketahui F'(x)=9x^2+4x-7 dan F(2)=5

Diketahui $F^{'} (x) = 9 x^{2} + 4 x - 7$ dan $F (2) = 5$ . Rumus untuk fungsi $F (x) = \dots$

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

B. $3 x^{3} + 2 x^{2} - 7 x - 5$

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

D. $3 x^{3} + 2 x^{2} - 7 x + 5$

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

Penyelesaian

RUMUS: $f (x) = a x^{n} \to \int f (x) d x = \frac{a}{n + 1} x^{n + 1}$

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

Diketahui:

$F^{'} (x) = 9 x^{2} + 4 x - 7$

$F (- 2) = 5$

Jawab

$F^{'} (x) = 9 x^{2} + 4 x - 7$

$F (x) = \frac{9}{2 + 1} x^{2 + 1} + \frac{4}{1 + 1} x^{1 + 1} - 7 x + C$

$F (x) = \frac{9}{3} x^{3} + \frac{4}{2} x^{2} - 7 x + C$

$F (x) = 3 x^{3} + 2 x^{2} - 7 x + C$

Mencari nilai C

$F (- 2) = 5$

$5 = 3 (- 2)^{3} + 2 (- 2)^{2} - 7 (- 2) + C$

$5 = - 24 + 8 + 14 + C$

$5 = - 2 + C$

$7 = C$

Rumus $F (x)$

$F (x) = 3 x^{3} + 2 x^{2} - 7 x + 7$

Jawaban: A

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