Question

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




​

Answer 1

Evaluate:

`\: \: \: \: \: \: \displaystyle\int\rm {y}^(2) \sqrt[3]{y} \: dy`

`{\large\underline{\sf{Solution-}}}`

`\: \: \: \: \: \: \displaystyle\int\rm {y}^(2) \sqrt[3]{y} \: dy`

can be rewritten as

`\rm \:  =  \: \displaystyle\int\rm {y}^(2) * {\bigg(y\bigg) }^{(1)/(3) } \: dy`

`\rm \:  =  \: \displaystyle\int\rm {\bigg(y\bigg) }^{2 + (1)/(3) } \: dy`

`\rm \:  =  \: \displaystyle\int\rm {\bigg(y\bigg) }^{(6 + 1)/(3) } \: dy`

`\rm \:  =  \: \displaystyle\int\rm {\bigg(y\bigg) }^{(7)/(3) } \: dy`

`\rm \:  =  \: \frac{ {\bigg(y\bigg) }^{(7)/(3) + 1} }{(7)/(3) + 1 } + c`

`\rm \:  =  \: \frac{ {\bigg(y\bigg) }^{(7 + 3)/(3)} }{(7 + 3)/(3)} + c`

`\rm \:  =  \: \frac{ {\bigg(y\bigg) }^{(10)/(3)} }{(10)/(3)} + c`

`\rm \:  =  \:(3)/(10) {\bigg(y\bigg) }^{(10)/(3)} + c`