# What is the arc length of #f(x)=x^2/12 + x^(-1)# on #x in [2,3]#?

By signing up, you agree to our Terms of Service and Privacy Policy

To find the arc length of the function ( f(x) = \frac{x^2}{12} + \frac{1}{x} ) on the interval ([2,3]), you would use the formula for arc length:

[ L = \int_{a}^{b} \sqrt{1 + \left(f'(x)\right)^2} , dx ]

Where ( f'(x) ) is the derivative of ( f(x) ).

First, find ( f'(x) ): [ f'(x) = \frac{1}{6}x - \frac{1}{x^2} ]

Now, plug ( f'(x) ) into the formula: [ L = \int_{2}^{3} \sqrt{1 + \left(\frac{1}{6}x - \frac{1}{x^2}\right)^2} , dx ]

Now, integrate to find the arc length.

By signing up, you agree to our Terms of Service and Privacy Policy

- What is a solution to the differential equation #dy/dx=(1+x)(1+y)#?
- What is a solution to the differential equation #dy/dx=(1+x)/(xy)# with y(1)=-4?
- How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region #y=2-x#, #2<=x<=4# rotated about the x-axis?
- How do you find the arc length of the curve #y = 4 ln((x/4)^(2) - 1)# from [7,8]?
- How do you find the surface area of the solid obtained by rotating about the #x#-axis the region bounded by #y=e^x# on the interval #0<=x<=1# ?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7