Question

Parameterizing a function

Answer 1

Line integral(x²-y+3z)ds

Answer 2

I don't understand how to find the bounds of integration...

Answer 3

given the parameters x=t, y=2t, and z=t

Answer 4

\[ \int(x^2-y+3z)ds\]
from which point to which point??

Answer 5

the line segment goes from (0,0,0) to (1,2,1)

Answer 6

change all x, y's and z's into t's

Answer 7

\[ ds = \sqrt{ \left ( \frac{dx}{dt} \right )^2 + \left ( \frac{dy}{dt} \right )^2+\left ( \frac{dz}{dt} \right )^2} dt\]
Change ds into above .., then integrate

Answer 8

Hm... my problem is determining the bounds of integration, as they are dependent on the parameters one chooses. Could you tell me how this is supposed to be done?

Answer 9

the logic behind it

Answer 10

to find bounds find values of t which gives (0,0,0) and (1,2,1)

Answer 11

the parametric equation of the line is given by
\[ r(t) = (0,0,0) + t(1,2,1) \]

Answer 12

yes

Answer 13

x=t, y=2t, and z=t
solve for (0,0,0) and (1,2,1)

Answer 14

in t=0 you will have (0,0,0)
and t=1 (1,2,1)

Answer 15

so your bounds are from 0 to 1

Answer 16

@EbnorEqvine

Answer 17

Ah, thank you, myko. So, what I'm trying to do is integrate the function over the interval on which t produces the endpoint values?

Answer 18

yes

Answer 19

Thank you very much!

Answer 20

yw