Penyelesaian:
[tex]\sf\int\limits^{4}_{1} {3x}^{2} + {3x}^{2} - {4x}^{3}[/tex]
[tex] = \int^{4}_{1}6 {x}^{2} - 4 {x}^{3} \\ = \frac{6}{2 + 1} {x}^{2 + 1} - \frac{4}{3 + 1} {x}^{3 + 1} |^{4}_{1} \\ = 2 {x}^{3} - {x}^{4} |^{4}_{1} \\ = (2(4 {)}^{3} - {4}^{4} ) - (2(1 {)}^{3} - {1}^{4} ) \\ = (2(64) - 256) - (2 - 1) \\ = 128 - 256 - 1 \\ = - 128 - 1 \\ = - 129[/tex]
[tex] \boxed{ \colorbox{black}{ \sf{ \color{lightgreen}{ answered\:by\:Duone}}}} [/tex]
Pembahasan :
[tex]\sf\int\limits^{4}_{1} {3x}^{2} + {3x}^{2} - {4x}^{3} \\[/tex]
[tex] = \displaystyle \sf \int 3x {}^{2} + 3x { }^{2} - 4x {}^{3} \: dx[/tex]
[tex] = \displaystyle \sf \int6x {}^{2} - 4x {}^{3} \: dx[/tex]
[tex] = \displaystyle \sf \int6x {}^{2} \: dx - \displaystyle \sf \int 4x {}^{3} \: dx[/tex]
[tex] = 2x {}^{3} - x {}^{4} [/tex]
[tex] = 2 \times 4 {}^{3} - 4 {}^{4} -(2 \times 1 {}^{3 } - 1 {}^{4} )[/tex]
[tex] = 2 \times 64 {}^{} - 256 {}^{} -(2 \times 1 {}^{ } - 1 {}^{} )[/tex]
[tex] = 2 \times 64 {}^{} - 256 {}^{} -1[/tex]
[tex] = 128- 256 {}^{} -1[/tex]
[tex] = - 129[/tex]
*lampiran = langkah pengerjaan ke-5 ( lanjutan 2x³ - x⁴ )
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