[tex] \boxed{\begin{aligned} \sf f(x)&=\sf 3 {x}^{3} + \frac{5}{2 } {x}^{2} - 2x + 25 \end{aligned}}[/tex]
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PEMBAHASAN
Diketahui:
[tex]{\begin{aligned}\sf \bull \: \: f(x) &=\sf \int( {9x}^{2} + 5x - 2) \: dx\\ \sf &=\sf \frac{9}{2 + 1} {x}^{2 + 1} + \frac{5}{1 + 1} {x}^{1 + 1} - 2x + C \\ \sf &= \sf \frac{9}{3} {x}^{3} + \frac{5}{2} {x}^{2} - 2x + C \\ \sf f(x)&=\sf 3 {x}^{3} + \frac{5}{2 } {x}^{2} - 2x + C \end{aligned}}[/tex]
[tex]\sf \bull \: \: f(2) = 5[/tex]
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Ditanyakan:
f(x) = ___?
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Penyelesaian:
[tex]\begin{aligned}\sf f(x)&=\sf \sf 3 {x}^{3} + \frac{5}{2 } {x}^{2} - 2x + C\\ \sf f(2)&=\sf 3(2 {)}^{3} + \frac{5}{2} ( {2)}^{2} - 2(2) + C \\ \sf 5&= \sf 3(8) + \frac{5}{2} (4) - 4 +C \\ \sf 5&=\sf 24 + 10 - 4 + C\\ \sf 5&=\sf 30 + C\\ \sf C&=\sf 30 - 5\\ \sf C&=\sf 25\end{aligned}[/tex]
Sehingga:
[tex]\sf f(x)=\sf 3 {x}^{3} + \dfrac{5}{2 } {x}^{2} - 2x + C [/tex]
[tex] \boxed{\begin{aligned} \sf f(x)&=\sf 3 {x}^{3} + \frac{5}{2 } {x}^{2} - 2x + 25 \end{aligned}}[/tex]
Jawaban:
f(x)= 3x³+5/2x²-2x+25
Penjelasan dengan langkah-langkah:
Integrasikan:
f(x)= 9/3x³+ 5/2x²-2x+C
f(x)= 3x³+5/2x²-2x+C
f(2)= 5
3(2)³+5/2(2)²-2(2)+C= 5
3(8)+5/2(4)-4+C= 5
24+3/2(4)+C= 5
24+6-C= 5
30-C=5
C= 25
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