What is the arclength of #f(x)=x/e^(3x)# on #x in [1,2]#?
The arc length is calculated from the following integral:
which leads us to
I haven't found an analytic expression for the integral. However, when we plot the function
What is deceiving about this graph is that arc-length is calculated in normal Cartesian space, which implies that the scale of
This implies that the actual arc length between 1 and 2 will be very close to the distance on the axis. Doing the integration numerically, one gets
which is very close to 1 as expected. A possible refinement would be to approximate the arc length with a straight line between