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Evaluate the following intergration:
∫y³ 3√(y.dy)




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Evaluate The Following Intergrationy 3ydy class=

Sagot :

SalmonWorldTopper

Evaluate:

[tex] \: \: \: \: \: \: \displaystyle\int\rm {y}^{2} \sqrt[3]{y} \: dy[/tex]

[tex] {\large\underline{\sf{Solution-}}}[/tex]

[tex] \: \: \: \: \: \: \displaystyle\int\rm {y}^{2} \sqrt[3]{y} \: dy[/tex]

can be rewritten as

[tex]\rm \:  =  \: \displaystyle\int\rm {y}^{2} \times {\bigg(y\bigg) }^{\dfrac{1}{3} } \: dy[/tex]

[tex]\rm \:  =  \: \displaystyle\int\rm {\bigg(y\bigg) }^{2 + \dfrac{1}{3} } \: dy[/tex]

[tex]\rm \:  =  \: \displaystyle\int\rm {\bigg(y\bigg) }^{\dfrac{6 + 1}{3} } \: dy[/tex]

[tex]\rm \:  =  \: \displaystyle\int\rm {\bigg(y\bigg) }^{\dfrac{7}{3} } \: dy[/tex]

[tex]\rm \:  =  \: \dfrac{ {\bigg(y\bigg) }^{\dfrac{7}{3} + 1} }{\dfrac{7}{3} + 1 } + c[/tex]

[tex]\rm \:  =  \: \dfrac{ {\bigg(y\bigg) }^{\dfrac{7 + 3}{3}} }{\dfrac{7 + 3}{3}} + c[/tex]

[tex]\rm \:  =  \: \dfrac{ {\bigg(y\bigg) }^{\dfrac{10}{3}} }{\dfrac{10}{3}} + c[/tex]

[tex]\rm \:  =  \:\dfrac{3}{10} {\bigg(y\bigg) }^{\dfrac{10}{3}} + c[/tex]

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