Calculate the area between two functions where x is element [0, 2pi:
f(x) = sinx + 1
g(x) = cosx + 1

Whenever I try the formula for calculating the area with both functions ( [integral from 0 to 2pi] f(x)-g(s) dx )

I get 0. Is 0 the answer, and how do I get to the answer?

Thank you :)

Question

Calculate the area between two functions where x is element [0, 2pi>:
f(x) = sinx + 1
g(x) = cosx + 1

Whenever I try the formula for calculating the area with both functions ( [integral from 0 to 2pi] f(x)-g(s) dx )

I get 0. Is 0 the answer, and how do I get to the answer? 

Thank you :)

anonymous · Answer

sinx +1 and cos x +1 intersect at pi/4 and 5pi/4

anonymous · Answer

in that interval, sinx +1 is top, and cosx +1 is at the bottom, 
however, [0, pi/4) you have cosx +1 is on top
and [5pi/4, 2pi) cosx +1 is on top
so that you have to break it into 3 parts to take integral

anonymous · Answer

https://www.desmos.com/calculator/ee8qbvlvrb

anonymous · Answer

Ah, I understand how to calculate the area. Now I know there is a method for checking when it intercepts each other, however I do not recall which method. How did I do that again?

anonymous · Answer

I think it was sinx+1 = cosx+1 :P

ganeshie8 · Answer

yes :) that gives you intersectios, a rough sketch is necessary to get a feel whats going on :

anonymous · Answer

Thank you