Use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the given curves about the y-axis. y = 13 e**(-x**2) text(, ) y = 0 text(, ) x = 0 text(, ) x = 1 v = sketch the region and a typical shell. (do this on paper. your instructor may ask you to turn in this sketch.)

As per the given statement:

The region bounded by the given curves about the y-axis, , y=0, x = 0 and x = 1

Using cylindrical shell method:

The volume of solid(V) is obtained by rotating about y-axis and the region under the curve y = f(x) from a to b is;

  where

where x is the radius of the cylinder

f(x) is the height of the cylinder.

From the given figure:

radius = x

height(h) =f(x) =y=

a = 0 and b = 1

So, the volume V generated by rotating the given region:

therefore, the volume of V generated by rotating the given region is

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