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I'm I on the right track here?

## Homework Statement

Evaluate the definite integral, if it exists

## Homework Equations

[tex]\int^{2}_{0}\stackrel{dx/}{(2x-3)^2}[/tex]

## The Attempt at a Solution

Let u = 2x-3

du = 2dx

1/2du = dx

[tex]1/2\int^{2}_{0}\stackrel{du/}{u^2}[/tex]

going back to our original u substitution: u = 2x - 3

= 2(0) - 3 = -3

= 2(2) - 3 = 1

[tex]1/2\int^{-3}_{1}\stackrel{du/}{u^2}[/tex]

[tex]1/2\int^{-3}_{1}\stackrel{du/}{(u^3)/3}[/tex]

(1/6) x du/(u)^3

[(1/6) x du/(1)^3] - [(1/6) x du/(-3)^3]

[(1/6) x du] - [(1/6) x du/(-27)]