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Problem in cylindrical shell

  1. Apr 18, 2009 #1
    y=x^4, y=sin(pix/2); about x=-1

    the solution is attached .

    how he determinate it to be from 0 to 1 ...???
    as I know , we usually put for example the expression of y1 = y2 and solve it for zero but in this case is not easy to do it,so how did he do it...??







    note: my english is bad so please correct any thing wrong in my writing...thanks.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Apr 18, 2009 #2

    Astronuc

    User Avatar

    Staff: Mentor

    y=x^4, y=sin(pix/2) intersect at 0 and 1, and looking at the shaded area in the figure, that is the area bounded (between) the two curves (function).
     
  4. Apr 18, 2009 #3
    may you show me the procedure of equaling the two equations step by step

    thanks
     
  5. Apr 18, 2009 #4

    Mark44

    Staff: Mentor

    You're right about the difficulty of solving an equation such as sin(pi * x/2) = x^4. Equations like this, where x appears in the argument of a transcendental function and outside it, are usually impossible to solve by algebraic means. I suspect that the author of this problem cooked up these functions so they would intersect at the origin and (1, 1).
     
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