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

1 Answer
Dec 7, 2015

3sqrt(5)

Explanation:

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)