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Math Help - Integration

  1. #1
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    Integration

    Def Int from 4-9 (x^1/2 + x^-1/2)^2 dx
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by bgonzal8 View Post
    Def Int from 4-9 (x^1/2 + x^-1/2)^2 dx
    first expand the brackets. using, of course, (a + b)^2 = a^2 + 2ab + b^2

    Then use the power rule for integrals to integrate, then continue with the fundamental theorem of calculus.

    do ou think you can do the problem now?
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  3. #3
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    I did do that and I still got stuck.
    I got ... the def. integral from 4-9 of (2x^1/4 + 2x^-1/4)dx so that equals

    (8x^5/4)/5 +3/(8x^3/4) + C. The main reason for my confusion is that the question is in the section of my textbook dedicated to Ln(x) so I thought that it was supposed to be part of the answer.
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  4. #4
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    (x^{\frac{1}{2}} +x^{\frac{-1}{2}})^2=(\sqrt{x}-\frac{1}{\sqrt{x}})^2

    You have expanded out the x^1/2 terms incorrectly. You will indeed end up with a log term. Think about what (\sqrt{x})^2 is.
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  5. #5
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    I see that that would make the radical disappear but when I expand it with foil I don't get that as any of the terms. i tried it again and I'm getting x^1/4 +2(sqrt(x))/(sqrt(x)) +x^1/4. And I dont think that's right.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by bgonzal8 View Post
    I see that that would make the radical disappear but when I expand it with foil I don't get that as any of the terms. i tried it again and I'm getting x^1/4 +2(sqrt(x))/(sqrt(x)) +x^1/4. And I dont think that's right.
    (x^{1/2} + x^{-1/2})^2 = (x^{1/2})^2 + 2x^{1/2}x^{-1/2} + (x^{-1/2})^2 = x + 2 + x^{-1}
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  7. #7
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    Ok, so (\sqrt{x})^2= x and \sqrt{x}=x^{\frac{1}{2}}.

    Try writing your function out as  (\sqrt{x} +\frac{1}{\sqrt{x}})^2, rather than ( x^{\frac{1}{2}}+x^{\frac{-1}{2}})^2
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  8. #8
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    Oh jeeze. Thanks you very much. It's always the algebra that gets me.
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