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Thread: Clarification on an identity of function

  1. #1
    Newbie AdarshK's Avatar
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    Clarification on an identity of function

    Hi,
    On my Notes of problem regarding surface area of revolution
    There is a Step
    Cosh2(x/c) integrating this

    In next step it written as (c/2)sinh2(x/c)

    The identity used is integ{cos2x} = sin2x/2

    But I can't apply this one in solving that step.
    I want to know how the "c" in (c/2) came on integrating


    Please have a look at this !!
    Last edited by AdarshK; Oct 12th 2017 at 07:04 AM.
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  2. #2
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    Re: Clarification on an identity of function

    Quote Originally Posted by AdarshK View Post
    Hi,
    On my Notes of problem regarding surface area of revolution
    There is a Step
    Cosh2(x/c) integrating this
    In next step it written as (c/2)sinh2(x/c)
    The identity used is integ{cos2x} = sin2x/2
    But I can't apply this one in solving that step.
    I want to know how the "c" in (c/2) came on integrating.
    I see that this is your first post, welcome.
    Now it is almost imperative that you post the entire original question.
    What you have have posted is some incomplete step of a solution.
    We have no way of knowing if that step is correct if we don't know the original question.
    Thanks from AdarshK
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  3. #3
    Newbie AdarshK's Avatar
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    Re: Clarification on an identity of function

    Thank You.

    The question is about finding surface area by generated by revolving about the x axis

    Q: Find area of the surface generated by revolving the arc of the catenary " y=ccosh(x/c) from x=0 to x=c about the x axis


    My approach on Note : the surface area equation using integration

    I think I can't write more of the answer steps . its very complex to text in keyboard

    Please reply if any other info needed
    Thank you.
    Last edited by AdarshK; Oct 12th 2017 at 07:36 AM.
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  4. #4
    Newbie AdarshK's Avatar
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    Re: Clarification on an identity of function

    Sorry that the title of my thread is misleading one . no option to edit now. This problem mainly dealing with "integration step doubt"
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  5. #5
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    Re: Clarification on an identity of function

    Q: Find area of the surface generated by revolving the arc of the catenary " y=ccosh(x/c) from x=0 to x=c about the x axis
    surface area of revolution ...

    $\displaystyle S = 2\pi \int_a^b f(x) \sqrt{1 + [f'(x)]^2} \, dx$

    $f(x) = c \cdot \cosh\left(\dfrac{x}{c}\right)$

    $f'(x) = c \cdot \sinh\left(\dfrac{x}{c}\right) \cdot \dfrac{1}{c}$

    $[f'(x)]^2 = \sinh^2\left(\dfrac{x}{c}\right)$

    $\displaystyle S = 2\pi \int_0^c c \cdot \cosh\left(\frac{x}{c}\right) \sqrt{1+ \sinh^2\left(\dfrac{x}{c}\right)} \, dx$

    note $1+ \sinh^2\left(\dfrac{x}{c}\right) = \cosh^2\left(\dfrac{x}{c}\right)$

    $\displaystyle S = 2\pi \cdot c \int_0^c \cosh^2\left(\frac{x}{c}\right) \, dx$

    note that $\cosh^2(u) = \dfrac{1+\cosh(2u)}{2}$

    can you finish from here?
    Thanks from AdarshK
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  6. #6
    Newbie AdarshK's Avatar
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    Re: Clarification on an identity of function

    Wow that really helped . i missed to take c as constant thank you so much
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