What is the arc length of #f(x)= sqrt(x^3+5) # on #x in [0,2]#?
The length is around
The formula for arc length of a curve of a function
Let us first work out
I will use the chain rule and let
Now we plug this into our arc length formula:
This function doesn't have an elementary anti-derivative (that I've been able to find). The best we can really do is use an approximation. Here I did a midpoint Riemann rectangle sum with 25 rectangles to get an answer of about