• Mar 13, 2012, 07:52 PM
xMerlina
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...
• Mar 19, 2012, 11:16 AM
ebaines
First please note that you 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 $(2-t)\sqrt t$

1. $2 \sqrt t - t^{\frac 3 2}$
2. Integrate: $\frac 4 3 t^{\frac 3 2} - \frac 2 5 t^{\frac 5 2}$
3. Evaluate on the interval [0,2]: $\frac 4 3 2^{\frac 3 2} - \frac 2 5 2^{\frac 5 2} \ = \ \frac 4 3 \times 2 \sqrt 2 - \frac 2 5 \time 4 \sqrt 2$

4. = $\frac 8 3 \sqrt 2 - \frac 8 5 \sqrt 2 \ = \ \frac {16} {15} \sqrt 2$

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