Question

What is the arc length of the curve given by `f(x)=1+cosx` in the interval `x in [0,2pi]`?

Answer 1

The arc length is most nearly `7.64` units.

Explanation:

Recall that arc length is given by `A = int_a^b sqrt(1 + (dy/dx)^2) dx`.

The derivative of `f'(x)` is `f'(x)= -sinx`.

`A = int_0^(2pi) sqrt(1 + (-sinx)^2)dx`

`A = int_0^(2pi) sqrt(1 + sin^2x)`

An approximation using a calculator gives `A = 7.64`.

Hopefully this helps!