7.3 prob 3 Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the y-axis:

Question

y=5e^(-x)^2, y=0, x=0, x=1.1

The circumference of a typical shell= 2pix

The height of this shell= 5e^(-x^2)

Thus the volume V= ?

and dx= ?

I figured out the answers to the first two, but now I'm stuck. What would the answers be to the last two?

Answer 1

V= 2π∫₀^1.15xe^{-x^2}dx = -10π∫₀^1.1du/2 where u= e^{-x^2} and du =- 2xe^{-x^2}dx so V = -5πe^{-x^2}|₀^1.1 and

V= -5π(e^-1.21 -1) V= 5π(1-1/e^1.21).