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-   -   Rewrite a fractional exponent as a radical when evaluating a definite integral? (http://www.askmehelpdesk.com/math-sciences/rewrite-fractional-exponent-radical-when-evaluating-definite-integral-643357.html)

  • 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

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

    4. =

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