Rewrite a fractional exponent as a radical when evaluating a definite integral?
 

Basically, I can't figure out how on earth my Calc teacher got his answer. The problem is:

integrate (2-t)√t dt on the interval [0.2]
1. 2t^(1/2) - t^(3/2)
2. 4/3t^(3/2) - 2/5t^(5/2) on the interval [0,2]
3. plugging in, I get 4/3*2^(3/2) - 2/5*2^(5/2) - 0
4. This is where I get lost. Somehow he got (8√2)/3 - (8√2)/5, which simplifies to (16√2)/15. I understand the fist half before the minus sign, but I don't understand the 2/5*2^(5/2) to (8√2)/5 at all....

First please note that yuo can't cuts and paste math formulas from other applications into this site - otherwise it displays gibberish.

I think what you're asking is this: Integrate

1.
2. Integrate:
3. Evaluate on the interval [0,2]:

4. =