Problem in cylindrical shell

moaath · Apr 18, 2009

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

Astronuc · Apr 18, 2009

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).

moaath · Apr 18, 2009

may you show me the procedure of equaling the two equations step by step

thanks

Mark44 · Apr 18, 2009

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...??

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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Problem in cylindrical shell

moaath

Attached Files:

Picture 5.png

Astronuc

Staff: Mentor

moaath

Mark44

Staff: Mentor

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