Question

Find the volume of the solid generated by revolving the regions bounded by the lines and curves
y= e^(-x/11) , y = 0, x = 0 and x = 11 about the x-axis.

Answer 1

Here, the cross section area will be an error function so should do i take the limit of the sums . Because it is asking for the exact answer .

Answer 2

is there a way to find the exact answer by using the simsons or trapezoidal rule.

Answer 3

hmm no you won't get the error function, thats only if you have to integrate e^(x^2)
\[\large (e^{-x/11})^{2} = e^{-2x/11}\]
so volume then is:
\[\large V = \pi \int\limits_{0}^{11}e^{-2x/11} dx\]