Jawaban:
[tex]\displaystyle\rm~ \frac{1}{9} [/tex]
Penjelasan dengan langkah-langkah:
[tex]\begin{aligned} \displaystyle\rm~\int~ \frac{2}{3} {x}^{5} ~dx & = \displaystyle\rm~ \frac{ \frac{2}{3} }{5 + 1} {x}^{5 + 1} + C \\ \\ & = \displaystyle\rm~ \frac{ \frac{2}{3} }{6} {x}^{6} + C \\ \\ & = \displaystyle\rm~ \frac{1}{9} {x}^{6} + C \end{aligned}[/tex]
[tex]\begin{aligned}\displaystyle\rm~ \int_{0}^{1} ~ \frac{2}{3} {x}^{5} ~dx & = \displaystyle\rm~ \frac{1}{9} {x}^{6}~ \Bigr|_{0}^{1} \\ \\ & = \displaystyle\rm~( \frac{1}{9} {(1)}^{6} ) - (\frac{1}{9} {(0)}^{6}) \\ \\ & = \displaystyle\rm~ \frac{1}{9} - 0 \\ \\ & = \displaystyle\rm~ \frac{1}{9} \end{aligned}[/tex]
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Jawaban:
[tex]\displaystyle\rm~ \frac{1}{9} [/tex]
Penjelasan dengan langkah-langkah:
[tex]\begin{aligned} \displaystyle\rm~\int~ \frac{2}{3} {x}^{5} ~dx & = \displaystyle\rm~ \frac{ \frac{2}{3} }{5 + 1} {x}^{5 + 1} + C \\ \\ & = \displaystyle\rm~ \frac{ \frac{2}{3} }{6} {x}^{6} + C \\ \\ & = \displaystyle\rm~ \frac{1}{9} {x}^{6} + C \end{aligned}[/tex]
[tex]\begin{aligned}\displaystyle\rm~ \int_{0}^{1} ~ \frac{2}{3} {x}^{5} ~dx & = \displaystyle\rm~ \frac{1}{9} {x}^{6}~ \Bigr|_{0}^{1} \\ \\ & = \displaystyle\rm~( \frac{1}{9} {(1)}^{6} ) - (\frac{1}{9} {(0)}^{6}) \\ \\ & = \displaystyle\rm~ \frac{1}{9} - 0 \\ \\ & = \displaystyle\rm~ \frac{1}{9} \end{aligned}[/tex]