Calculating Line Integral of Lamda Curve

[MaxManus]

Homework Statement

A curve lamda starts in (0,0) and fallows a straight line from x = 0, y = 0 to x = 1, y = 0 and then another straight line to x = 2 and y = 1. Calculate the line integral I = S vdr
where S is an integral s
v = (x+3y)i + (3+y)j

Homework Equations

The Attempt at a Solution

the first line
y = 0
dy = 0
S x dx from 0 to 1
= 1/2

The second line
x = t
y = t
dx = dt
dy = dt

S (t+3t)dt + (3+t)dt
and here it stops. Both x and y are variables and x are supposed to go from 1 to 2 and y from 0 to 1.

 

[Dick]

x=t and y=t doesn't parametrize the line connecting (1,0) and (2,1), does it?

 

[MaxManus]

then there is something I have got wronge. I have not done much of parametrization, but I was thinking a straight line from (1,0) to (2,1) had to be 45 degrees and the you used x = t and y = t which gives 45 degree angle.

 

[Dick]

It's 45 degree's alright but if you put t=0, you get (0,0). How about putting x=t+1?

 

[MaxManus]

So it is?

x = t+1
y = t
dx = dt
dy = dt
S t+1 + 3t + 3 + t dt
S 5t + 4 dt from 0 to 1
= 13/2

Thanks for all the help