# Thread: Area under curve question

1. ## Area under curve question

Ok, so the equation is $\displaystyle y=(x^2-1)e^x$, $\displaystyle y=0, x=-1, x=1$, 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 $\displaystyle x^2e^x - e^x - 2xe^x + 2e^x$ which simplified to $\displaystyle e^x (x^2 -2x +1)$ which I evaluated from -1 to 1. The problem is that my answer came out to be $\displaystyle -4/e$ 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!

2. Originally Posted by emttim84
Ok, so the equation is $\displaystyle y=(x^2-1)e^x$, $\displaystyle y=0, x=-1, x=1$, 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 $\displaystyle x^2e^x - e^x - 2xe^x + 2e^x$ which simplified to $\displaystyle e^x (x^2 -2x +1)$ which I evaluated from -1 to 1. The problem is that my answer came out to be $\displaystyle -4/e$ 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