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F'(x) = 6x2 - 2x + 5 dan F(-2) = -12

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Tentukan rumus fungsi F(x) jika diketahui:

F'(x) = 6x² - 2x + 5 dan F(-2) = -12

Jawab: 

F'(x) = 6x² – 2x + 5

F(x) = ∫ (6x² – 2x + 5) dx

F(x) = 2x³ – x² + 5x + C

F(-2) = 2(-2)³ – (-2)² + 5(-2) + C

⇔ -12 = 16 – 4 – 10 + C

⇔ -12 = 2 + C

⇔ C = -14

Jadi F(x) = 2x³ – x² + 5x – 14

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