Evaluating Line Integral: ∫(x+2y)dx+(x^2)dy

[ahhppull]

Homework Statement

Evaluate the line integral ∫(x+2y)dx+(x^2)dy, where C consists of the line segments from (0,0) to (2,1) and (2,1) to (3,0)

Homework Equations

The Attempt at a Solution

I'm unsure of what to do. I did (1-t)r0 + t(r1) for (0,0) to (2,1) and (2,1) to (3,0). I didn't get the answer, which is 5/2 however.

 

[LCKurtz]

Homework Statement

Evaluate the line integral ∫(x+2y)dx+(x^2)dy, where C consists of the line segments from (0,0) to (2,1) and (2,1) to (3,0)

Homework Equations

The Attempt at a Solution

I'm unsure of what to do. I did (1-t)r0 + t(r1) for (0,0) to (2,1) and (2,1) to (3,0). I didn't get the answer, which is 5/2 however.

Show us your work and we will help you find what went wrong.

 

[ahhppull]

Honestly, I have no idea what to do, but here what I did.

From (0,0) to (2,1)
r(t) = (1-t)<0,0> + t<2,1>
r(t) = <2t,t>

x=2t
y=t

I found that the integral is from 0 to 1.

dx/dt = 2
dy/dt = 1

∫(x+2y)dx+(x^2)dy
Then I set x as 2t and y as t into the equation:


=∫[(2t+2t)(2)+(4t^2)(1)]dt
=∫(8t+4t^2)dt
= 4t^2 +4/3t^3 ] <-----evaluate from 0 to 1
= 4 + 4/3
= 16/3

Then I did this same thing for the from (2,1) to (3,0) and added the two numbers.

 

[haruspex]

= 16/3
Then I did this same thing for the from (2,1) to (3,0) and added the two numbers.

I agree with 16/3, and I applied the same method for the second segment to get a total of 5/2. So your mistake must be in working you have not posted.