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Math Help - integration again...

  1. #1
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    integration again...

    i know this is integration by parts but not sure how to actually do it..

    integrate......... 2x sqrt(x) dx
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    Quote Originally Posted by b00yeah05 View Post
    i know this is integration by parts but not sure how to actually do it..

    integrate......... 2x sqrt(x) dx
    Why do you want to use integration by parts?

    \int (2x\sqrt{x}) dx = \int (2 \sqrt{x^5}) dx = \int (2 \cdot x^{\frac52}) dx

    I'll leave the rest for you!
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    where did you get the 5 from??????
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    Quote Originally Posted by b00yeah05 View Post
    where did you get the 5 from??????
    Sorry - it's too early in the morning here. Instead of 5 write 3. You should have then:

    \int (2 \cdot x^{\frac32}) dx
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    sorry..would you mind explaining how you got that?? im assuming you did...

    2 . x . sqrt(x) = 2 . sqrt(x^2)

    then 2 . (x^2)^1/2

    correct?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by b00yeah05 View Post
    sorry..would you mind explaining how you got that?? im assuming you did...

    2 . x . sqrt(x) = 2 . sqrt(x^2)

    then 2 . (x^2)^1/2

    correct?
    no. x \sqrt{x} is not \sqrt{x^2} (how did you get that??)

    x \sqrt{x} = x \cdot x^{1/2} = x^{1 + 1/2} = x^{3/2}
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    Quote Originally Posted by b00yeah05 View Post
    sorry..would you mind explaining how you got that?? im assuming you did...

    2 . x . sqrt(x) = 2 . sqrt(x^2)

    then 2 . (x^2)^1/2

    correct?
    Not quite:

    x = \sqrt{x^2}

    Therefore

    x \sqrt{x} = \sqrt{x^2} \cdot \sqrt{x} = \sqrt{x^2 \cdot x} = \sqrt{x^3} = x^{\frac32}
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  8. #8
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    i see so...the x at the front becomes x^1 = x . x^1/2 therefore......x^1+1/2 = x^3/2
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    Quote Originally Posted by b00yeah05 View Post
    i see so...the x at the front becomes x^1 = x . x^1/2 therefore......x^(1+1/2) = x^3/2
    Good job - and much easier than the calculations I did.

    But: Use parantheses!
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Krizalid View Post
    I think this topic it's pretty useless having this one which is also solved.
    indeed!
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  11. #11
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    Quote Originally Posted by Krizalid View Post
    I think this topic it's pretty useless having this one which is also solved.
    And, in a broader context, there's this one, where the elephant in the room actually gets pointed out.
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