# Line integral (flux)

## Homework Statement

for $$\varphi$$(x,y)=2x+y+10 ,calculate the flux line integral...on a straight line from A(1,4) to B(5,1).

## The Attempt at a Solution

I tried to solve it but didnt get the right answer.
first i found the quation of the line which i found to be y=-(3/4)*x
and then i set x=t (parameter) and insert t into the y equation=-(3/4)*t. 1<t<5
dx=dt;dy=-(3/4)dt

and i used the formula for line integral which is $$\int$$(2x+y+10)*(dy,-dx)
i subtituted the values for x,y,dx and dt in to the above equation and integrated over 5 to 1..
the right answer is 92. i got -9.

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Borek
Mentor
By mistake I have removed answer by hgfalling, sorry about that. Here it comes:

The equation of the line is definitely not y=-3x/4: the point (1,4) is on the line!

I'm not sure what your formula for the line integral is at all; is that supposed to be a dot product?
I suggest you parametrize your line correctly as a function r(t); it seems you are on the right track with this. Then

$$\intop_S f ds = \intop_a^b f(r(t)) |rsingle-quote(t)| dt$$