How do I approach this work in multiple dimensions question?

Question

The path of a particle is described by the position vector vec r =<3t, t^ 2 ,-t> . The particle experiences a force which varies as a function of the particle's position, described by the function vec f =<-2y, x^ 2, 3> . Determine the work done on the particle by the force from time t = 0 to t = 3 seconds.

Answer 1

Elementary work dw = f•dr = <-2t², 9t², 3>•<3,2t, - 1>dt = (- 6t² + 18t³ - 3)dt

So, W = ∫₀³(- 6t² + 18t³ - 3)dt = (- 2t³ + 4.5t⁴ - 3t)₀³ = - 54 + 364.5 - 9 = 301.5