Question

f(x,y) = x+2y. Evaluate scalar line integral over given path x. x(t)=(2-3t,4t-1), 0 14 years ago

Answer 1

wrt dx or dy or ds?

Answer 2

ds

Answer 3

the answer is 50, but im getting 54

Answer 4

(2-3t + 8t - 2)ds
5tds
ds = sqrt(25)

Answer 5

so u get
25tdt from t=0 to 2
get it?

Answer 6

sorry, you lost me at previous post

Answer 7

ohk
wts the formula for ds?

Answer 8

my teacher uses the equation \[\int\limits_{0}^{2} f(x(t))*(x'(t)) ds\]

Answer 9

so for this problem i got \[\int\limits_{0}^{2} (2-3t,4t-1) * (-3,4) dt\]

Answer 10

er should be (2-3t,8t-2)

Answer 11

is the answer 50??

Answer 12

yea..

Answer 13

then look

ure supposed to evaluate

f(x,y)ds arent u?

Answer 14

fox????????

Answer 15

convert f(x,y) to f(t) by replacing x and y by their parametric definitions ok?

Answer 16

ok

Answer 17

so f(x,y) reduces to what?

Answer 18

(2-3t,8t-2) ?

Answer 19

x+2y = 5t

Answer 20

ok

Answer 21

isnt it??

Answer 22

so now for ds

remember

\[ds = \sqrt{ (dx/dt)^2 + (dy/dt)^2} dt\]

Answer 23

so, sqrt(3^2+4^2)?

Answer 24

yes

Answer 25

which =5

Answer 26

so finally u have

\[\int\limits_{0}^{2}(5t)(5dt)\]

Answer 27

now its easy isnt it??

Answer 28

yea. thanks

Answer 29

welcome