# Finding the area between $f(x)=e^{x/2}-2$ and $g(x)=x^2+2x-1$, from $x=0$ to $x=2$

I need to find the area between the graphs of $$f(x)=e^{x/2}-2 \quad\text{and}\quad g(x)=x^2+2x-1$$ and the lines $$x = 0$$ and $$x = 2$$.

I think I need to do $$g(x)-f(x)$$ with $$0$$ and $$2$$ as the lower and upper limits on the integrals.

But how do I go forward with it?

• Your idea is fine but the assumption $g(x) \ge f(x)$ needs first to be proved. Also we need to be sure we are looking for the absolute area and not the signed area. – user Nov 2 '20 at 10:14

Yes your idea is fine, firstly we need to show that $$g(x)\ge f(x)$$ within the domain
$$\int_0^2 (g(x)-f(x))dx$$