Question

What is the arclength of `f(x)=xsin3x` on `x in [3,4]`?

Answer 1

`approx 6.578961133`

Explanation:

Given is
`f(x)=xsin(3x)`
We Need the product and the chain rule:

`f'(x)=sin(3x)+3xcos(3x)` so we have evaluate the following integral

`int_3^4sqrt(1+(sin(3x)+3xcos(3x))^2)dx`
a numerical method gives us

`approx 6.578961133`