Question

What is the arclength of `f(x)=2-3x` in the interval `[-2,1]`?

Answer 1

`3sqrt10`

Explanation:

`f(x)=2-3x`
`f"'"(x)=-3`

`L=int_a^b sqrt(1+[f"'"(x)]^2)*dx`
`L=int_-2^1 sqrt(1+9)*dx`
`L=sqrt10*x|_-2^1=sqrt10(1-(-2))=sqrt10(1+2)=3sqrt10`