Integrating a Line Integral with Parametric Equations

[animboy]

Homework Statement

Evaluate the line integral ∫_c y² dx + 2xy dy,

where C, is the path from (1, 2) to (2, 4) parametrised by

r(t) = (t² + 1)i + (2t² + 2)j , 0 ≤ t ≤ 1

Homework Equations

I worked out the velocity magnitude |v(t)| as 2t√5

The Attempt at a Solution

I simply integrated the velocity with respect to t from 0 to 1. and got 56, but then I don't see why I needed that first equation. Are we supposed to do dot product or something first?

 

[jedishrfu]

Aren't you supposed to get x( t) and y(t) from the 2nd eqn and to then sub it into the 1st to convert it to an integral in t from 0 to 1? And then solve it.