Area bounded by parametric equations

**Punch** · August 22nd 2011, 06:03 AM

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 $x=e^3$

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

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

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

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

$=e^3+e$

$=22.8 unit^2$

But answer is 9.34unit^2

**Danny** · August 22nd 2011, 06:21 AM

If you draw a picture of the region in question, you'll find that y is negative for t = 1 to 2 then goes positive. You'll need to split your integral up into two pieces to account for that.

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