## psk981 3 years ago Evaluate: Please look at the integral

1. psk981

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

2. psk981

from (2,4) to (1.1)

3. psk981

|dw:1352896610110:dw|

4. experimentX

along the straight line? what is T ?

5. psk981

you have to find flow

6. experimentX

|dw:1352897206497:dw|

7. psk981

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

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

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

10. amistre64

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

looks like chain rule

12. amistre64

this is a line integral right?

13. amistre64

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

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

15. psk981

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

16. amistre64

i believe we also need r'

17. psk981

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

18. psk981

r'(t)=-i-3j

19. amistre64

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

20. psk981

yes its F. dr/dt

21. psk981

i am not sure abt the dr/dt part

22. amistre64

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

23. amistre64

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

24. amistre64

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

25. amistre64

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

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

27. psk981

nope

28. amistre64

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

29. psk981

these vector fields so confusing

30. amistre64

indeed they are

31. psk981

i have another vector question

32. amistre64

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

how do i draw a vector field

34. amistre64

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