Q. 14.55
[tex] \\ [/tex]
[tex] \tt \int \: {x}^{5} \: {(2 - {x}^{3}) }^{ \frac{1}{2} } \: dx = ..[/tex]
[tex] \\ [/tex]
RULES :
[tex] \\ [/tex]
=> No NGASAL.
=> Ngasal ? report.
=> Pake Cara.
=> No copas.
=> RAPI.
[tex] \\ [/tex]
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[tex] \\ [/tex]
[tex] \tt \int \: {x}^{5} \: {(2 - {x}^{3}) }^{ \frac{1}{2} } \: dx = ..[/tex]
[tex] \\ [/tex]
RULES :
[tex] \\ [/tex]
=> No NGASAL.
=> Ngasal ? report.
=> Pake Cara.
=> No copas.
=> RAPI.
[tex] \\ [/tex]
Penjelasan dengan langkah - langkah:
[tex]\tt \int \: {x}^{5} \: {(2 - {x}^{3}) }^{ \frac{1}{2} } \: dx [/tex]
[tex] = \sf\tt \int \: {x}^{3} \: {(2 - {x}^{3}) }^{ \frac{1}{2} } \: dx [/tex]
[tex] \sf = \tt \int \: \: {(2 - {u}^{}) }(u {}^{ \frac{1}{2} } ) \frac{du}{ - 3} [/tex]
[tex] \sf = \frac{ - 1}{ 3} \tt \int \:2u {}^{ \frac{1}{2} } - u {}^{ \frac{3}{2} } du[/tex]
[tex] \sf = \frac{ - 1}{3} ( \frac{4}{3} u {}^{ \frac{3}{2} } - \frac{2}{5} u {}^{ \frac{5}{2} } ) + c[/tex]
[tex] \sf = \frac{ - 4}{9} u.u {}^{ \frac{1}{2} } + \frac{2}{15} u {}^{2} u {}^{ \frac{1}{2} } + c[/tex]
[tex]= \sf \frac{ - 4}{9} (2 - x {}^{2} ). \sqrt{2 - x {}^{3} } + \frac{2}{15} (2 - x {}^{3} ) {}^{2} \sqrt{2 - x {}^{2} } + c[/tex]
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