Negative area between two curves

[adriaat]

I've been trying to figure out what a negative area means, but I can't.

Homework Statement
Calculate the area between f(x) = 3^{x} \, , \, g(x)=2x+1

The attempt to a solution
The intersections are located in x=0 and x=1.
So I do the integral from 0 to 1.
\int_{0}^{1} (g(x)-f(x))dx = \frac{2}{log(3)}-2 \approx -0.17952154675

What am I doing wrong? I am integrating the upper function minus the lower function.

 

[ShayanJ]

The Negative is only telling that the function 3^x-2x-1,has negative values more than positive ones inside the interval of integration and of course by integrating 2x+1-3^x you will get a positive answer!It is obvious from this that the sign doesn't mean much.

 

[pbuk]

\int_{0}^{1} (g(x)-f(x))dx = \frac{2}{log(3)}-2

No, you have swapped f(x) and g(x) in this step.