# area between 2 functions

• Jan 23rd 2011, 03:55 PM
maybnxtseasn
area between 2 functions
i havent taken calculus for a few years now and i need step by step on 1 problem i was assigned

1.) i need to find the area between these 2 functions
---------------------------------------------------------
f(x) = cosx
g(x) = 2-cosx 0 <= x <= 2(pi)
• Jan 23rd 2011, 03:58 PM
Prove It
You won't get step by step here I'm afraid, but the first thing to do would be to graph the functions, see which points on the domain $\displaystyle \displaystyle f(x) > g(x)$, which points on the domain $\displaystyle \displaystyle g(x) > f(x)$.

Then, the Area is $\displaystyle \displaystyle \int_a^b{f(x) - g(x)\,dx}$ (if $\displaystyle \displaystyle f(x) > g(x)$)
• Jan 23rd 2011, 04:14 PM
maybnxtseasn
found my problem....calculator was on degrees and not radians
• Jan 23rd 2011, 04:20 PM
chisigma
Quote:

Originally Posted by maybnxtseasn
i havent taken calculus for a few years now and i need step by step on 1 problem i was assigned

1.) i need to find the area between these 2 functions
---------------------------------------------------------
f(x) = cosx
g(x) = 2-cosx 0 <= x <= 2(pi)

With simple 'geometrical' considerations You can find that the area between the figures is...

$\displaystyle \displaystyle A= 2 \int_{0}^{2 \pi} (1-\cos x)\ dx$ (1)

... the solution of which is immediate...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$
• Jan 24th 2011, 04:58 AM
HallsofIvy