# Homework Help: Substitution of a definite integral

1. Feb 4, 2012

### bobsmith76

1. The problem statement, all variables and given/known data

3. The attempt at a solution

I don't see why the √v disappears in this step

I understand how they got the 20/3, because they integrated, but if they're integrating then I would think v^-1/2 would become (v^1/2)/(1/2)

Last edited: Feb 4, 2012
2. Feb 4, 2012

### Curious3141

The √v disappears because $dv = \frac{2}{3}v^{-\frac{1}{2}}du$ (rearranging the equation they gave for du). Substitute that for dv into the integrand and you'll see why. The 20/3 comes from 10*(2/3) during this substitution, NOT from integration (which hasn't occurred yet).