Line integral Question

1. Jul 26, 2011

stratusfactio

1. The problem statement, all variables and given/known data

calculate the integral f · dr for the given vector field f(x, y) and curve C:
f(x, y) = (x^2 + y^2) i; C : x = 2 + cos t, y = sin t, 0 ≤ t ≤ 2π (2pi)

2. Relevant equations

Would the vector F simply be <(x^2+y^2),0> since there is no j component?
The solution is 4pi and I'm getting zero.

3. The attempt at a solution
integral of C = F · dr
F = <((2+cos t)^2 + (sin t)^2),o> = <(5 + 4 cos t), 0>
dr = <-sin t, cos t>

Integral of C [0, 2pi] <(5 + 4 cos t), 0> · <-sin t, cos t> = 0 :(

I'm thinking that my error lies in the vector I'm using for F.

2. Jul 26, 2011

HallsofIvy

Staff Emeritus
If the problem is exactly as you stated, then the correct answer is 0.

3. Jul 26, 2011

thepatient

That's right, the F vector function only has a i component. It would be equivalent as writing it as F(x,y) = <x^2 + y^2, 0>

BTW I posted this same exact problem. :P where did you find this?

4. Jul 26, 2011

thepatient

5. Jul 26, 2011

stratusfactio

^Haha. I'm self teaching myself Multivariable Calculus using this online book: http://www.mecmath.net/calc3book.pdf in conjuction with Youtube's UCBerkely Multivariable Calc lectures.

It's just weird because I did all the steps and analyzed each step and can't see where I went wrong...we may be right because I see you got 0 too, sometimes the books make errors. I just don't see how we can get 4pi when we're evaluating an integral involving trig. when it's going to give us a rational number.

6. Jul 27, 2011

thepatient

I was doing the same with that same book. :P There were a few other errors too in other parts. I think the book just needs more revising.