# Area bounded by parametric equations

• Aug 22nd 2011, 07:03 AM
Punch
Area bounded by parametric equations
The curve $L$ is defined by the parametric equations

$x=e^t$ , $y=t-2$

Find the area of the region enclosed by the curve $L$, the x-axis and the lines $x=e$ and $x=e^3$

$Area=\int^{e^3}_et-2dx$

$\frac{dx}{dt}=e^t$

$Area=\int^{3}_1(t-2)e^tdt$

$=((3-2)e^3)-((1-2)e)$

$=e^3+e$

$=22.8 unit^2$