What is the arc length of #f(x)=sin(x+pi/12) # on #x in [0,(3pi)/8]#?
The arclength is around
To calculate the actual arclength, we'll need to get an integral in the form of
(This link does a great job of explaining arc lengths of function graphs.)
To get that integral, first, calculate
Now, plug this into the aforementioned integral and put the appropriate bounds. You will see that the
At this point, you should probably plug this integral into a calculator because the function probably doesn't have an antiderivative, and even if it does, it would be a pain to calculate.
A calculator should spit out something around