Question

Consider the vector field F(x) = . Evaluate the path integral, where C is the line segment beginning at the point (0, pi/2) and ending at the point (2, pi). I cannot figure out how to start this problem. Help, please?

Answer 1

find a parametric curve that gives said line segment

Answer 2

note going from \((0,\pi/2)\to(2,\pi)\) yields a direction vector \(\langle2,\pi/2\rangle\) so we may parameterize the path as \(\vec{r}(t)=\langle0,\pi/2\rangle+t\langle2,\pi/2\rangle\) for \(t\in[0,1]\)

Answer 3

you have a vector field that produces vectors thru a straight line ... sum up all the normals thru the line

Answer 4

I am getting a really weird integral - still confused. :/

Answer 5

hmm amistre64?

Answer 6

Ahh, sorry to make things difficult. I've been stuck on this problem and another one for the past 3 hours. I have all of the others done, but I've hit a dead end with the last two.

Answer 7

@ashnaveed93 recall the line integral essentially quantifies how 'in phase' our vector field is with our curve:$$\int_C e^x\langle\sin y,\cos y\rangle\cdot d\vec{r}$$

Answer 8

Hm, so you would take the dot product of F with the derivative of r⃗ (t)=⟨0,π/2⟩+t⟨2,π/2⟩, and let t∈[0,1] be the limits?