Integration of trigonometry (1 Viewer)

[lolitaaa]

Hey everyone! Can you please help me with this trigonometry question? There are many intersections of the curves and do I need tofind them?

Find the area enclosed between the curves y=sin x and y=cos x in the domain between 0 and 2pi?

 

[braintic]

Firstly, the question is unclear. It is not clear whether they want the area totally enclosed by the two curves, or whether they also want the regions that have x=0 and x=2pi as a boundary. But if you draw a diagram, you should be able to see that the second case gives an area that is twice the first. I will assume the first case.

There are not 'many' points of intersection of the curves ... only two ... at x=pi/4 and x=3pi/4.

So the area of the region totally enclosed by those two curves is the integral between those two limits of (sinx - cosx) dx.
Double that if it is to be interpreted in the second way.