How do you use the method of cylindrical shells to find the volume generated by rotating the region bounded by #y=e^(−x^2)#, y=0, x=0, and x=1 about the y axis?

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Answer 1 · 2015-10-12T20:14:05

Draw a sketch, then integrate using the shell method with respect to x.

Here is sketch of the problem:

enter image source here

Using the formula for the Shell Method:

#2piint_0^1(x)(e^(-x^2)-0)dx#

You can use substitution {#u=x^2#} to solve.

#=pi(1-e^-1)#

Answer #~~1.986#

Hope that helps