## psk981 Group Title Evaluate: Please look at the integral one year ago one year ago

1. psk981 Group Title

$\int\limits_{C}^{} F.T ds$ for a vector field F=x ^{2}i-yj

2. psk981 Group Title

from (2,4) to (1.1)

3. psk981 Group Title

|dw:1352896610110:dw|

4. experimentX Group Title

along the straight line? what is T ?

5. psk981 Group Title

you have to find flow

6. experimentX Group Title

|dw:1352897206497:dw|

7. psk981 Group Title

how did u get r(t) i know you used the points but why did u pick t for the second set of points

8. amistre64 Group Title

the t used is just a variable scalar to stretch the vector to all point along the line from the point used to anchor it to the line

9. psk981 Group Title

so how would i find F. dr/dt where T=dr/dt?

10. amistre64 Group Title

i dont recall the flow stuff to clearly, but does this look familiar? $\frac{dr}{dt}=\frac{dr}{dx}\frac{dx}{dt}+\frac{dr}{dy}\frac{dy}{dt}$

11. psk981 Group Title

looks like chain rule

12. amistre64 Group Title

this is a line integral right?

13. amistre64 Group Title

http://tutorial.math.lamar.edu/Classes/CalcIII/LineIntegralsVectorFields.aspx ive always found this to be a rather good read. so im going over it

14. psk981 Group Title

r(t)= <2-t, 4-3t>

15. psk981 Group Title

F=(2-t)^2i-(4-3t)j

16. amistre64 Group Title

i believe we also need r'

17. psk981 Group Title

how would i get it i know its a derivative would it be r(t)= -i-3j

18. psk981 Group Title

r'(t)=-i-3j

19. amistre64 Group Title

then thats its; dot F and r' together to get a scalar equation to integrate right?

20. psk981 Group Title

yes its F. dr/dt

21. psk981 Group Title

i am not sure abt the dr/dt part

22. amistre64 Group Title

r= <2-t, 4-3t> r'= <(2-t)', (4-3t)'> r'= <-1, -3>

23. amistre64 Group Title

F=<(2-t)^2 ,-4+3t> dot r'=< -1 , -3 > ----------------------- -(2-t^2)+12-9t

24. amistre64 Group Title

got me ^2 in the wrong side ... :/

25. amistre64 Group Title

the line is from t=0 to t=1 giving us$\int_{0}^{1}-4-t^2+4t-9t+12~dt$$\int_{0}^{1}-t^2-5t+8~dt$

26. amistre64 Group Title

do you have an answer key to check with by chance?

27. psk981 Group Title

nope

28. amistre64 Group Title

well, weve followed the simple directions from pauls site; so it should be good ;)

29. psk981 Group Title

these vector fields so confusing

30. amistre64 Group Title

indeed they are

31. psk981 Group Title

i have another vector question

32. amistre64 Group Title

the Force equation gives us the force at each for each x,y point along the line the lines vector equation gives us the x and y values along the path F(r) is just defining the forces along the path; dotting with r' tho has me a little baffled at an explanation at the moment tho ;)

33. psk981 Group Title

how do i draw a vector field

34. amistre64 Group Title

for each lattice point on a graph you draw a little arrow indicating the direction and magnitude of the vector associated with the values of x and y (or whatever reference frame your using) at that point