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Volumes of Rotation

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    Prove that the volume of a solid generated by completely rotating the function y= 6/(2x + 1)^1/2 about the x-axis, x=0 and x=4 is 36pi ln3 units cubed

    y^2= 36/ (2x+ 1)^1/4

    V = pi [18ln(2x+1)^1/4] with 4 at top of bracket and 0 at bottom

    just wondering what you do with the power in this case 1/4???
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    \left(\dfrac{6}{(2x + 1)^\frac{1}{2}} \right)^2 \neq \dfrac{36}{(2x+ 1)^\frac{1}{4}}

    Remember that \sqrt{a} \times \sqrt{a}=a
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    (Original post by Kvothe the Arcane)
    \left(\dfrac{6}{(2x + 1)^\frac{1}{2}} \right)^2 \neq \dfrac{36}{(2x+ 1)^\frac{1}{4}}

    Remember that \sqrt{a} \times \sqrt{a}=a
    duh thanks

    when i do it properly i then get
    [(18ln9} - (18 ln1)]
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    (Original post by Custardcream000)
    duh thanks
    when i do it properly i then get

    [(18ln9} - (18 ln1)]
    Remember that a \ln b^n=an \ln b
    And \ln a - \ln b = \ln \frac{a}{b} or more simply that \ln1=0
 
 
 
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