Calculate line integrals with parametrization

Question

anonymous · Answer

attachment

anonymous · Answer

well the equation can be parameterized as following: 
R(t)=(x(t), y(t))= (0,3t) or R(t)=3tj
F=3i+(y+5)j      F(t)=3i+(3t+5)j

anonymous · Answer

so now i need to find the line integral

turingtest · Answer

ok let me have my notes handy

anonymous · Answer

so its Int (F*dr)

anonymous · Answer

so it wld be int (3i+(3t+5)j)*(3)

anonymous · Answer

like i kinda guessed this stuff so idk
int(3+9t+15)

anonymous · Answer

hahaha i think i will just come back on a diff account :PPP

turingtest · Answer

3j, right?
so we are just dotting those two

anonymous · Answer

yes

anonymous · Answer

idk i am assuming

anonymous · Answer

does it look correct?

anonymous · Answer

im back again

turingtest · Answer

as far as I can tell

anonymous · Answer

so it wld be (18t+9/2t^2) with the upper limit 1 and the lower limit 0

turingtest · Answer

grr...
I wanna say 'yes' but I'm not sure, I'm rusty on this
so I'm looking at my notes to make sure

anonymous · Answer

thanks

turingtest · Answer

the i-part goes away with the dot product

turingtest · Answer

$$\int(3\hat i+(3t+5)\hat j)\cdot 3\hat jdt=\int_{0}^{1}9t+15dt$$unless I am misreading something, it's really that simple

anonymous · Answer

ohhhh ok that is what i assumed

anonymous · Answer

ohhhh ok i get it now

anonymous · Answer

yup i seee my mess up

turingtest · Answer

yeah, the dot product kills that i-component in this case
that was your only mistake

anonymous · Answer

alrighty thanks turing U R AWESOME as usual

turingtest · Answer

NO!
you are welcome $and$ awesome!