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Math Help - find integral of this

  1. #1
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    find integral of this

    integral( 1/sqrt(x),x, 0,1) = 2sqrt(x)
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  2. #2
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    Quote Originally Posted by szpengchao View Post
    integral( 1/sqrt(x),x, 0,1) = 2sqrt(x)
    \int_0^1 \frac{dx}{\sqrt{x}} = \int_0^1 x^{-1/2} dx.
    Now use the exponent rule.
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  3. #3
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    how

    how to?
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    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by szpengchao View Post
    how to?
    Power Rule:

    \int u^n \,du = \frac{u^{n+1}}{n+1}

    Does that help?
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  5. #5
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    ..

    i mean from definition.... is it the only way to find integral?
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  6. #6
    Moo
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    Quote Originally Posted by szpengchao View Post
    i mean from definition.... is it the only way to find integral?
    Mmmm... remember the derivative of \sqrt{t} ?

    It's \frac{1}{2 \sqrt{t}}, recognize it in the integral
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  7. #7
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    well

    i do it by riemann integrable.

    define LRS and URS, i suceed to show LRS=URS, but cant show that LRS=2sqrt(a)

    m...so we can say, becoz derivative of sqrt(x) is that, so the definite integral =2sqrt(x)
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  8. #8
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    You cannot use the Riemann integral over here. The function \frac{1}{\sqrt{x}} is even defined on [0,1]. If you had [1,2] then it is possible to do it by definition, but not the way you posted the problem.
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