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Math Help - Approximate value of integral

  1. #1
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    Approximate value of integral

    Find the length "L" of a certain curve given by L=

    - Im having a hard time with this, any help with be very appreciated
    -thanks
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  2. #2
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    Make the following substitution:
    u = 4+ 3x
    du = 3dx \: \: \Rightarrow \: \: dx = \frac{du}{3}

    Also, we must change our limits of our integral:
    u(8) = 4 + 3(8) = 28
    u(2) = 4 + 3(2) = 10

    So substituting all these in:
    = \int_{u(2)}^{u(8)}\! \sqrt{u} \frac{du}{3} \: = \: \frac{1}{3} \int_{10}^{28} u^{\frac{1}{2}}du
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  3. #3
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    Im sorry im very new to integrals, and need to see all the steps involved in solving this problem so I have an idea on what to do on future problems.
    -Thank you
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    This is a must-know integral: \int x^{n} dx = \frac{x^{n+1}}{n+1} + C where n \neq -1 and is some constant.

    Do you not see how that applies to the last integral I gave you?
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  5. #5
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    is the answer 6.28?
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  6. #6
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    I think i figured this out.. is the correct answer 25.8976?
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  7. #7
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    From where we last left off:
    \frac{1}{3} \int_{10}^{28} u^{\frac{1}{2}}du = \frac{1}{3} \cdot \frac{u^{\frac{3}{2}}}{\frac{3}{2}}  \bigg|_{10}^{28} \: \: = \: \: \frac{2}{9} u^{\frac{3}{2}} \bigg|_{10}^{28} \: \: = \: \: \frac{2}{9} \left( 28^{\frac{3}{2}} - 10^{\frac{3}{2}} \right) \: \approx \:  25.898

    Just as you had
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  8. #8
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    That's the correct answer Eric08.

    See QuickMath, pretty useful for cheking answers.
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  9. #9
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    Quote Originally Posted by Krizalid View Post
    That's the correct answer Eric08.

    See QuickMath, pretty useful for cheking answers.
    You can check answers on Graph 4.3 as well. The only problem is it does not always have "nice" answers like QuickMath does.
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