# Thread: Area between two curves (simple question)

1. ## Area between two curves (simple question)

Hi,

I'm trying to find the area between the curves:

y=x^2 + 4x +1 and
y = 3x+3

A sketch shows me that y =3x+3 is above y=x^2 +4x +1 and I have found the intersection points are x=-2 and x=1.

Does this then mean that I just need to evaluate the integral of (3x+3)-(x^2+4x+1) from -2 to 1?

I know that some of this area lies underneath the x-axis and not sure if I need to be accounting for that or not.

Thanks!

2. ## Re: Area between two curves (simple question)

Hi Andy, you don't have to worry if one of the graphs is below the x-axis. In fact, both graphs can be below the x axis and the definite integral ∫ [higher function] - [lower function] dx = area between the curves still holds. So you're right, just evaluate the integral you said before.

3. ## Re: Area between two curves (simple question)

Thanks very much