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Math Help - "Find the volume of a solid..."

  1. #1
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    "Find the volume of a solid..."

    "find the volume of a solid generated by revolving about the line y=1 the region in the first quadrant bounded by the parabolas 3x^2-16y=0 and x^2-16y+96=0 and the y axis."

    The caveat here is I have dysgraphia and need to conceptualize this without manually drawing graphs if at all possible. Currently the easier problems in the section take me 30-45 minutes to graph, etc.

    Second problem is:

    "Find the volume of a solid generated by revolving the region in the first quadrant bounded by the curve y^3=x^4 and the X axis" with part A being revolving the region around the line x=8 and part B around the line Y=16.

    In particular, I'm not sure where my limits of integration are coming from nor where, in the part B, the example problem has a constant squared.

    We didn't work this level of problems in class and I'll be bothering my instructor about these ( previous lesson had some surprise problems too! ). Our textbook is completely and totally useless as well. ( They did one semester of calc 1s on it, then rolled it out. So this semester is the only calc 2 class in it and the next the only calc 3 class )
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  2. #2
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    So, why am I subtracting 1 from both the parabolas ( in y= form ) in the first problem, and in the second problem, what's up with the limits of integration ( I.E. part A it's 0 to 16, part B it isn't doubled, it's 0 to 16 again IIRC ), and why in part B, when I solve for Y=x^3/4, am I integrating from 0 to 8 ((16^2) - (16 - x^3/4 ) )^2 all multiplied by pi?

    I'm not even sure why I'm subtracting x^3/4 from 16, and my book ( "Calculus, Early Trascendentals, by Varberg, Purcell, and Rigdon" ) is useless at explaining the concept behind it as it uses exclusively high brained vocabulary to the point I have to try to rewrite what it's saying - literally translate it - at times.
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