So for example, take:
$y = 2x$ on the interval $[0,1]$ around the $x$-axis.
The volume should be $4π/3 u^3$.
Now rotating $y = 2x$ on the interval $[0,1]$ around the $y$-axis:
1) Rewrite the function: $x = y/2$.
2) Recalculate limits: $[0,2]$.
I get: $4π/3 u^3$ -again!
Is this true with all functions and axes?
I ask because, I'm studying for a test and can't seem to find examples of the same function being rotated around different axes. Often times I get different results.
I appreciate your time, I believe many others are wondering the same.
Thanks!