Homework Help

a. write and simplify the integral that gives the arc length of the curve on the given...

user profile pic

user5369070 | eNotes Newbie

Posted June 17, 2013 at 3:37 PM via web

dislike 2 like

a. write and simplify the integral that gives the arc length of the curve on the given integral y=1/x (1,10)

1 Answer | Add Yours

user profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted June 17, 2013 at 4:54 PM (Answer #1)

dislike 0 like

The arc length of a smooth curve f(x) on the interval [a,b] is given by:

`s=int_a^b sqrt(1+[f'(x)]^2)dx`

Here `f(x)=1/x ==> f'(x)=-1/x^2` so

`s=int_1^(10) sqrt(1+1/x^4)dx`

The approximation for s is `s~~9.153`

**The integral does not "simplify" in terms of the basic trigonometric, exponential, or polynomial functions.**

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes