How do you find the arc length of the curve y=lnxy=lnx from [1,5]?

1 Answer
Sep 12, 2015

The arc length is defined by the following formula: L=int_1^5 sqrt{(x^2+1)/(x)}dxL=51x2+1xdx

Explanation:

To find the arc length of a curve, we use the formula
L=int_a^b sqrt{1+[f'(x)]^2}dx

In our case, f(x) = ln x, a=1, and b=5.
The derivative of f(x)=ln x is f'(x)=1/x, so we get:

L=int_1^5 sqrt{1+[1/x]^2}dx
L=int_1^5 sqrt{1+1/(x^2)}dx
L=int_1^5 sqrt{(x^2+1)/(x)}dx