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Math Help - rotational solids confusing me

  1. #1
    Junior Member
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    rotational solids confusing me

    question :

    give the volume of the solid generated by revolving the region bounded by the graph of y=ln(x), the x-axis, the lines x=1 and x=e, about the y axis.


    I dont understand because im like... about the y axis ? If I rotate all of the lines about the y axis it really doesnt make sense to me. If I rotate ln(x) around y axis itll look like a cone, then x=1 would be like a cylander around it, and x=e would be an even bigger cylinder around that... then they say the x axis... So Im like you cant rotate the x axis about the y axis right ?

    It makes sense to me with it being ln(x) around the X axis with x=1 and x=e around the x axis cutting off pieces of it, then take the area from ln(x) to the x axis (or 1/2 the total area).

    So yeah can anyone give me some insight? Maybe they meant x axis ?
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  2. #2
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    You're rotating the region bounded by these curves about the y-axis. Look at similar questions to get an idea of what volume is being generated. This problem is best solved using the shell method.
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  3. #3
    Super Member Quacky's Avatar
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    If x=1, then y=ln(1)
    If x=e, then y=ln(e)

    If y=ln(x), then x=e^y

    See this page for hints - the bottom example is almost identical!
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