How do i find the area of of the region bounded by the curve y=e^2x, the x-axis, and x=2

i know you need to integrate it but i'm not sure how to set it up.

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- Jun 2nd 2010, 01:27 AMwolfxpaxarea between a line and a curve
How do i find the area of of the region bounded by the curve y=e^2x, the x-axis, and x=2

i know you need to integrate it but i'm not sure how to set it up. - Jun 2nd 2010, 02:07 AMHallsofIvy
I presume that you know that the "area under a curve", the area between the graph and the x-axis, between, say, x= a and x= b, is the integral of the function from a to b. In this case, there is only one x bound given but $\displaystyle y= e^{2x}$ goes to 0 as x goes to negative infinity so that the

**three**lines, $\displaystyle y= e^{2x}$, y= 0, and x= 2 do bound a "region". The area is $\displaystyle \int_{-\infty}^2 e^{2x} dx$. Integrate $\displaystyle \int_a^2 e^{2x} dx$ and then take the limit as a goes to negative infinity.