# Area between two curves

For this problem there are two functions
f(x) = cos x
g(x) = 2-cos x
where 0<x<2π
I know this is probably fairly simple, but we just started learning this stuff
I know the equation ∫f(x) - g(x) or ∫top-bottom curve, but if you graph it, you can see that it's not that simple (I think)

#### skeeter

MHF Helper
For this problem there are two functions
f(x) = cos x
g(x) = 2-cos x
where 0<x<2π
I know this is probably fairly simple, but we just started learning this stuff
I know the equation ∫f(x) - g(x) or ∫top-bottom curve, but if you graph it, you can see that it's not that simple (I think)
yes, it's that simple ...

$$\displaystyle A = \int_0^{2\pi} (2-\cos{x}) - \cos{x} \, dx$$

• Not that big a number. When $$\displaystyle x= \pi$$, cos(x)= -1 so 2- cos(x) is 3 and cos(x)= -1. If you put a rectangle about that figure, it would have height 4 and width $$\displaystyle 2\pi$$, so area $$\displaystyle 8\pi$$. It looks reasonable that the area between the two curves is half the area of the rectangle containing them.