Question

Evaluate the line integral, where C is the given curve.

Answer 1

\[\int\limits \over c \] x sin y ds, C is the line segment from (0, 1) to (3, 5)

Answer 2

is it 1.5{cos1 - 5 cos5}?
i'm not sure

Answer 3

how did you find it? Are the parametric equations x=3t and y=3+4t

Answer 4

0<=t<=1

Answer 5

the equation of the curve is: y-1=(4/3)(x)
express the integrand in terms of y
then, ds=\[\sqrt{(dx)^2+(dy)^2}\]
take dy common and then, what we get is: \[dy \sqrt{(dx/dy)^2+1}\], dx/dy is the inverse of the slope of the curve, then evaluate

Answer 6

i use this approach unless there are multiple integrals in the problem and if you wish to use the parametric equations, they should be: x=t and y=(4/3)t+1, 0<t<3

Answer 7

also, we do not use teh equality sign as you did, that is to say: we should not write it this way, 0<=t<=3, because they are limits, the variables always tend to the limits, so you can get rid of the equality sign :)

Answer 8

ok, why is t from 0-3?

Answer 9

and how did you get the parametric equations?

Answer 10

t is from 0-3 because i put x=t and the parametric equation, well, teh curve c here, is the line segment having the given end-points, right?
so, write the equation of the line segment, equate one of the variables to t and then find the other in terms of it

Answer 11

ok, I think I understand that

Answer 12

wonderful! using your information to evaluate the integral worked. Thank you. :)

Answer 13

welcome :)