How do I parametrize a line integral with vector functions?

[iScience]

(disregard the [5+5+5] in the question)attempt:
dr=(e^t(cost)+(sint)e^t)$\hat{i}$ + (-e^t(sint)+(cost)e^t)$\hat{j}$

∫<3+2xy, x²-3y²>$\cdot$<e^t(cost)+(sint)e^t, -e^t(sint)+(cost)e^t>dt

..at which point i remembered i had to parametrize F in terms of t, but didn't know how to do

 

[Simon Bridge]

you want to integrate only over those values of x and y that lie on the curve mapped out by r(t) ... so what determines if a point (x,y) is on r?

 

[iScience]

to answer your question, it would be if curve C lies if the domain of F, i don't see how this would help me though, I'm trying to put the vector field in terms of t.

 

[iScience]

you want to integrate only over those values of x and y that lie on the curve mapped out by r(t)

i would have to put the curve that is in terms of t, into some function of x and y then, how?

 

[iScience]

this was a stupid question. Sorry, i just figured it out...

 

[Simon Bridge]

Well done :)