integral (3x³- 4x)dx​

integral (3x³- 4x)dx​

Penjelasan dengan langkah-langkah:

[tex] = \int(3 {x}^{3} - 4x) \: dx[/tex]

[tex] = \frac{3}{3 + 1} {x}^{3 + 1} - \frac{4}{1 + 1} {x}^{1 + 1} + c[/tex]

[tex] = \frac{3}{4} {x}^{4} - \frac{4}{2} {x}^{2} + c[/tex]

[tex] = \frac{3}{4} {x}^{4} - 2{x}^{2} + c[/tex]

Penyelesaian

[tex]f(x) = 3x^3 - 4x[/tex]

[tex]=\frac{x^{n+1}}{n+1}[/tex]

[tex]\int (3x^3 - 4x) , dx = 3 \int x^3 , dx - 4 \int x , dx[/tex]

[tex]= 3 \left( \frac{x^{3+1}}{3+1} \right) - 4 \left( \frac{x^{1+1}}{1+1} \right)[/tex]

[tex]= 3 \left( \frac{x^4}{4} \right) - 4 \left( \frac{x^2}{2} \right)[/tex]

[tex]= \frac{3}{4} x^4 - 2x^2 + C[/tex]