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    Hi,

    Could some kind mathematician provide me with a step-by-step integration to show the volume of a cylinder, which has been generated from a
    rectangle that lies on the x-axis with limits of 0 to h.

    Failing that, could you please start me off with the function that describes this rectangle of y=? and x=h and I might be able to do the integration myself.

    Thanking you in advance,

    Kevin
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    Let y=r be the equation, where r is the radius of the surface.
    If we integrate between 0 and h, then h is the height of the cylinder.
    Volume of revolution = \fs4 \pi \int^h_0 r^2.dx = \pi [r^2x]^h_0 = \pi r^2.h, as desired.
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    Hi,

    THANK YOU - Your superb solution makes it look easy.

    Can you briefly explain why integrating r^2 does not become r^3/3
    but r^2 * x as in your example.

    Sorry for being so obtuse, but I am a newbie to calculus.

    Cheers,

    Kevin
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    You are not integrating with respect to r, because the radius is fixed. You are integrating along the axis of the cylinder, where the variable is the height of the cylinder, not the radius.

    Notice that the integral is \int r^{2}.dx NOT \int r^{2}.dr
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    Thank you for your input AlphaNumeric and also CA>O7.

    Being a beginner regards calculus, I was hoping for a step-by-step solution so that I could see where the "x" came from when R² got integrated.

    Am I right in saying that the integral should read ∫ PI x 1 x R² dx and when the constants are placed out of the integral sign, becomes PI x R² ∫ 1 dx.

    ∫ 1 dx therefore becomes the "x" whose presence I could not understand.

    Thanks for being so patient with a neophyte !

    Cheers,

    Kevin
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    (Original post by zorrozac)
    Am I right in saying that the integral should read ∫ PI x 1 x R² dx and when the constants are placed out of the integral sign, becomes PI x R² ∫ 1 dx.
    Yep, that is true. If something isn't a function of the letter after the "d" (like functions of x and dx or functions of t and dt) then you can just pull it out infront of the integral sign. Since Pi and R are constants, they aren't functions of anything, so you can bring them out the front
 
 
 
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