# What is the arc length of #f(x)=-xln(1/x)-xlnx# on #x in [3,5]#?

##### 1 Answer

Mar 13, 2017

#### Explanation:

Use the rule

#f(x)=-xln(x^-1)-xln(x)#

Bringing the

#f(x)=xln(x)-xln(x)#

#f(x)=0#

This is the straight line

Using

#L=int_a^bsqrt(1+(f'(x))^2)dx#

#L=int_2^4sqrt(1+0)dx#

#L=int_2^4dx#

#L=x]_2^4#

#L=2#