# Math Help - Line integral

1. ## Line integral

Could use some help in evaluating this line integral....

$
\int\limits_\Upsilon {\{ [\exp (x^2 /y^2 ) + xy^2 ]dx + [(y^6 /x) + (x/y^3 )]dy\} }
$

where the path r is the line ${y^2 }$ = x, from (1,1) to (4,2)

2. Originally Posted by reivera
Could use some help in evaluating this line integral....

$
\int\limits_\Upsilon {\{ [\exp (x^2 /y^2 ) + xy^2 ]dx + [(y^6 /x) + (x/y^3 )]dy\} }
$

where the path r is the line ${y^2 }$ = x, from (1,1) to (4,2)
First you need to parameterize the curve

let $y=t$ then $x=t^2$ $t \in [1,2]$

Note: there are many other ways we have parameterized this.

Now we can compute dy and dx

$dx=2tdt \mbox{ and } dy=dt$

now we just substitute in to the above and evalute

$\int_{1}^{2}\left( e^{t^2}+t^4\right)(2t)dt+\left( t^4+\frac{1}{t}\right)dt$

Now it is off to the races.

Good luck.