What is the arc length of #f(x)=2x-1# on #x in [0,3]#?

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Answer 1 · 2015-12-07T00:21:03

#3sqrt(5)#

Arc length can be found using the integral;

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

You can find the derivation of this formula here . To start, we need to know the derivative, #f'(x)#, which can be found using the power rule.

#d/dx (2x-1) = 2#

Now we can set up the integral.

#L = int_0^3 sqrt(1+2^2)dx#

#= int_0^3 sqrt(5)dx#

#= sqrt(5)int_0^3 dx#

#= sqrt(5)[x]_0^3#

#= 3sqrt(5)#