Question

how do you solve this problem?
y=2, y=lnx, find the volume around the y axis, all values in the first quadrant?
ans: pi(e^4-1)/2
drawing an approximate picture.

Answer 1

@campbell_st can you help?

Answer 2

yep... volume around the y axis is

\[V = \pi \int\limits_{a}^{b} x^2 dy\]

so you are integratign between y = 0 and y = 2

if y = ln(x)

then

\[x = e^y\]

so the volume is

\[V = \pi \int\limits_{0}^{2} (e^y)^2 dy\]

hope this helps

Answer 3

thank you!