Question

Value of the Line integral of xe^y dx over arc of x=e^y from pt (1,0) to (e,1). Please don't bother if you don't know how to do it. Thanks

Answer 1

parametize C of the line integral as

`({e}^(t) ,t)`
from 0<=t<1 then

`dx = {e}^(t) dt`
which means by substituting x with e^t and y with and dx with e^t dt we get

`integral \: from \: 0 \: to \: 1( {e}^(t) * {e}^(t) * {e}^(t) \: dt )`
by adding exponents

`integrl \: from \: 1 \: to \: 0 \: of \: ( {e}^(3t)dt )`

`\frac{ {e}^(3) - 1}{3} - \frac{ {e}^(0) - 1 }{3}`