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Math Help - Integration w/ u-substitution, work is inside

  1. #1
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    Integration w/ u-substitution, work is inside

    http://i36.tinypic.com/rsas13.jpg

    Thanks in advance for any help!
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  2. #2
    Member pflo's Avatar
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    Why use u-substitution on this problem?
    \int{t^2(t-\frac{2}{t}) dt}
    \int{(t^3-2t)dt}
    \frac{t^4}{4}-t^2+c

    I suppose if you HAVE to use u-substitution, you could let u=t^2 instead.
    That would give you the following integral:
    \int{(\frac{u}{2}-1)du}
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  3. #3
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    Quote Originally Posted by pflo View Post
    Why use u-substitution on this problem?
    Well, that's what the lesson was on, so I just assumed we had to do it that way. But yeah, that's easier. Does that mean u-sub would be nearly impossible/very difficult if I were to do it?
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  4. #4
    Member pflo's Avatar
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    Quote Originally Posted by janedoe View Post
    Well, that's what the lesson was on, so I just assumed we had to do it that way. But yeah, that's easier. Does that mean u-sub would be nearly impossible/very difficult if I were to do it?
    I edited my original reply to include a method where you could use u-substitution.

    One note: When using u-substitution, always look for the derivative of u (the one with the original variable) to cancel out. In this case, you identified the problem with the substitution you originally did - couldn't cancel out the t's. But with u=t^2 the derivative would include a 't' which WOULD cancel out.
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