Calculus Integration Question?

Question

I've been working on this problem all day (it is part of a definite integral word problem) and I have been trying to match up the answer with the answer I get in Maple. I never seem to come out right. I think the error is in my integration. I'm trying to integrate:
Pi*sqrt(y)*sqrt(4+(1/y))

Any advice is appreciated. Thanks

Answer 1

integral pi sqrt(y) sqrt(4+1/y) dy
= integral pi sqrt( 4y+1) dy
= (2/3)(1/4) pi (4y+1)^(3/2) + const

Answer 2

First, let's simplify the formula:

∫π√y√(4+1/y) dy

Becomes:

π∫√(4y+1) dy

Let us make the substitution u=4y+1, du=4 dy:

π/4 ∫√u du

Which integrates trivially as:

π/6 * u^(3/2) + C
π(4y+1)^(3/2)/6 + C

And we are done.

Answer 3

try this link on calculus help.. it should be in there okay!