Question

What is the arc length of `f(x)=(x^3 + x)^5` in the interval `[2,3]`?

Answer 1

`approx 2.42*10^7`

Explanation:

We Need the Formula

`s=int_a^bsqrt(1+(f'(x))^2)dx`

we have
`f'(x)=5(x^3+x)^4(3x^2+1)`
so our integral is given by

`int_2^3sqrt(1+(5(x^3+x)^4(3x^2+1))^2)dx`
this is `approx 2.42*10^7`