Question

Compute Line Integral: F= <2ysinx, -xsinx>, C has parameterization r(t)= for t between 0 and 1

Answer 1

\[\int\limits_{c}^{}F*dr\] in this form

Answer 2

@SolomonZelman @TuringTest

Answer 3

F=(2ysinx, -xsinx)
C as parameterization r(t)= (t, t^2)

Answer 4

@iambatman @Compassionate @abb0t

Answer 5

@iGreen @eliassaab

Answer 6

So we need to find F(r(t)) and also r'(t)
\[F(r(t))=F(x(t),y(t)) \\ \text{ where } x(t)=t \text{ and } y(t)=t^2 \\ \text{ so } F(r(t))=F(x,y)=F(t,t^2) \\ \text{ replace } x \text{ with } t \text{ and replace } y \text{ with } t^2 \\ \text{ so } F(r(t))=<2t^2\sin(t), -tsin(t)>\]
Now you also need to find r'(t)
from r(t)=<t,t^2>

Answer 7

after that we will find the dot product of F(r(t)) and r'(t)

Answer 8

then integrate

Answer 9

alright

Answer 10

\[\int\limits_{0}^{1}F(r(t)) \cdot r'(t) dt \]

Answer 11

so r'(t)= 1, 2t

Answer 12

yea

Answer 13

so (1,2t)* (2t^2sint, -tsint)

Answer 14

\[<2t^2\sin(t),-tsin(t)> \cdot <1,2t>=?\]

Answer 15

yeah either way
<a,b> dot <c,d>=ac+bd
or
<c,d> dot <a,b>=ca+db

Answer 16

ok thanks

Answer 17

http://tutorial.math.lamar.edu/Classes/CalcIII/LineIntegralsVectorFields.aspx
never done line integrals
i was just using this as a guide :)

Answer 18

so then its 2t^2sint-2t^2sint

Answer 19

me neither lol

Answer 20

and yes exactly

Answer 21

im actually taking bc
the answer is 0

Answer 22

\[\int\limits_{0}^{1} (2t^2\sin(t)-2t^2\sin(t) ) dt \]

Answer 23

oh whoops

Answer 24

is that right?
let me look at it again

Answer 25

so isnt the answer simply 0? how do you integrate 0?

Answer 26

integrating 0 gives you a constant
because the derivative of a constant is 0
\[\int\limits_{0}^{1}0 dx=0\]

Answer 27

but integrating a 0 on an interval gives you 0
because you are looking at a rectangle with 0 height

Answer 28

i'm going to look back at this work

Answer 29

yeah thats what i thought

Answer 30

everything we did looks right
I just can't believe the answer is 0 :p

Answer 31

hmm.

Answer 32

anyways thanks for your time

Answer 33

im pretty sure the answer is correct

Answer 34

anyone else got anything?

Answer 35

I think 0 is right. I'm just getting afraid of the answer 0 because I felt like I have already seen it so much today.

Answer 36

it's been a right minute since I have done these, but I think @freckles is correct :)

Answer 37

ok thanks guys, gonna close