Integral help
y=cosx, y=2-cosx, 0

Question

Integral help
y=cosx, y=2-cosx, 0<x<2pi

I got 4pi + 1
Just need to confirm that

anonymous · Answer

There are two y's.

you need integral of what??

anonymous · Answer

I'm trying to find the area in-between the 2 curves

anonymous · Answer

in that interval of 0 to 2pi

anonymous · Answer

Sorry I have no clue..

anonymous · Answer

haha ok

anonymous · Answer

Can you show me your steps??
May be I can help you somewhat..

anonymous · Answer

$$2-\cos(x)\geq \cos(x)$$ so your area between the curves is found via 
$$\int_0^{2\pi}2-\cos(x)-\cos(x)dx=\int_0^{2\pi}2-2\cos(x)$$

anonymous · Answer

should be straightforward to compute, it is 
$$\int_0^{2\pi}2dx-2\int_0^{2\pi}\cos(x)dx$$ first part is $2\pi\times 2=4\pi$ from your eyeballs, second one is what you get when you take the anti derivative of sine, and evaluate

anonymous · Answer

satellite73 is correct.

hero · Answer

By the way @satellite73, I usually use my brain and a pencil to evaluate things. Not necessarily eyeballs

anonymous · Answer

sure but not $\int_a^b cdx=c(b-a)$