How do you integrate by substitution int 2piy(8-y^(3/2))dy?

1 Answer
Steve M
Nov 18, 2016

int 2piy(8-y^(3/2))dy = 2pi{ 4y^2 - 2/7y^(7/2)} + C

Explanation:

You do not need to use a substitution as the integral can be calculated "as is":

int 2piy(8-y^(3/2))dy = 2piint 8y-y^(5/2)dy
:. int 2piy(8-y^(3/2))dy = 2pi{ 8y^2/2 -y^(7/2)/(7/2)} + C
:. int 2piy(8-y^(3/2))dy = 2pi{ 4y^2 - 2/7y^(7/2)} + C

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