# Area under curve question

• Jan 22nd 2008, 05:33 PM
emttim84
Area under curve question
Ok, so the equation is $y=(x^2-1)e^x$, $y=0, x=-1, x=1$, problem is to find area under the curve. That's fine, but this is actually the first one I'm doing where the area in question is /under/ the X-axis, since I'm in calc 2 now.

I ended up getting $x^2e^x - e^x - 2xe^x + 2e^x$ which simplified to $e^x (x^2 -2x +1)$ which I evaluated from -1 to 1. The problem is that my answer came out to be $-4/e$ which is a negative value, which obviously can't be for area. In this instance, did I forget a step somewhere or do you just change the sign of the answer? Thanks!
• Jan 22nd 2008, 06:23 PM
polymerase
Quote:

Originally Posted by emttim84
Ok, so the equation is $y=(x^2-1)e^x$, $y=0, x=-1, x=1$, problem is to find area under the curve. That's fine, but this is actually the first one I'm doing where the area in question is /under/ the X-axis, since I'm in calc 2 now.

I ended up getting $x^2e^x - e^x - 2xe^x + 2e^x$ which simplified to $e^x (x^2 -2x +1)$ which I evaluated from -1 to 1. The problem is that my answer came out to be $-4/e$ which is a negative value, which obviously can't be for area. In this instance, did I forget a step somewhere or do you just change the sign of the answer? Thanks!

You did do it right....the negative simply means the area is below the x-axis