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

the answer is c

step-by-step explanation:

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b