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How do you find the arc length of the curve #y=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)}dx#

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#

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