Show that the area between the curves y=e^x and y=e^(2x) from x=0 to x=1 is given by (1/2e^2 - e +1/2).

Ive tried various times and only get 1/2 e^2 -e

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- Sep 7th 2009, 01:20 AMLukybearExponential Integration
Show that the area between the curves y=e^x and y=e^(2x) from x=0 to x=1 is given by (1/2e^2 - e +1/2).

Ive tried various times and only get 1/2 e^2 -e - Sep 7th 2009, 01:30 AMred_dog
$\displaystyle \int_0^1(e^{2x}-e^x)dx=\left.\frac{e^{2x}}{2}\right|_0^1-\left.e^x\right|_0^1=\frac{e^2}{2}-\frac{1}{2}-(e-1)=$

$\displaystyle =\frac{e^2}{2}-e+\frac{1}{2}$ - Sep 7th 2009, 01:52 AMLukybear