Definite Integral Length of vector r(t)

[jimbo71]

Homework Statement

Evaluate the integral length of r(t)=[tihat +t^2jhat]dt from 0 to 2

Homework Equations

The Attempt at a Solution

I think I should find the length of r(t) first which would be sqrt(t^2ihat+t^4jhat). However I'm not sure how I would integrate sqrt(t^2ihat+t^4jhat).

 

[Mark44]

You can also write r(t) as (x(t), y(t)), where it's understood that this is a vector in R^2. Here x(t) = t and y(t) = t^2. For arc length between t = 0 and t = 2, your integral should be:
$$\int_0^2 \sqrt{(dx/dt)^2 + (dy/dt)^2} dt$$