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Math Help - Help with Area and Volume problems

  1. #1
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    Help with Area and Volume problems

    I have exams coming up, and need some help with some homework problems that I'm really having difficulties with. I would appreciate either a step by step or something to get me on my way. Thanks!

    2. Find the volume of the solid formed when the region bounded by the curves y=x^3+1, x=1 and y=0 is rotated about the x-axis. How do I do something like this for a volume of the solid problem with three curves???

    4. Find the area bounded by the curves f(x)=x^3+x^2 and g(x)= 2x^2+2x

    5. A cylindrical hole is drilled through the center of a sphere of radius R. Use the method of cylindrical shells to find the volume of the remaining solid, given that the solid is 6 cm high.

    24. Find the volume of the solid generated by revolving about the line x=-1, the region bounded by the curves y= -x^2 + 4x -3 and y=0.

    25. Consider the region in the xy-plane between x=0 and x=pi/2, bounded by y=0 and y=sin(x). Find the volume of the solid generated by revolving this region about the x-axis.

    30. Let R be the region bounded by y=(1/x), y=x^2, x=0, and y=2. Suppose R is revolved about the x-axis. Set up but do not evaluate the integrals for the volume of rotation using (a) the method of cylindrical shells; (b) the method of circular disks.
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  2. #2
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    Please don't post more than two questions in a thread. Otherwise the thread can get convoluted and difficult to follow. It is better for forum organization and better for you to get your questions answered in a more timely manner if you start new threads as necessary for remaining questions. eg. If you have five questions, post two of them in two threads and start a new thread for the remaining one etc.

    And if the question has more than two parts to it, it is best to post only that question and its parts in the thread and start a new thread for other questions.

    Thread closed.
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