2.1 Area Between Curves

[STARTS AT 16:47]

INSTRUCTOR: Next, we're going to do the same functions, different interval. All right. So the sketch of my graph for sine x-- now, this is from pi over 2 to 2 pi. All right. 

So in this case, pi over 2. So sine. There's pi. We're going to 2 pi. And cosine. 

So this area is going to break up. So here is pi over 2. The highest point, there. Pi over 2 to 2 pi. So we need a couple of regions. 

So this is going to be the integral of pi over 2 to, in this case, 5 pi over 4 is where those two intersect. Of-- and that would be sine minus cosine. That would be x plus 5pi over 4 to 2pi of, in that case, we have cosine is above. 

So cosine minus sine x dx. Now, these integrals are going to be the same as before. They're just going to be evaluated differently. So this is negative cosine x minus sine x. 

Pi over 2, to 5pi over 4, sine x plus cosine x evaluated from 5 pi over 4 to 2 pi. So we get square root of 2 plus 1, 1 plus square root of 2. That's great. 

Those are the same. So our area is 2 plus 2 square roots of 2 unit squared.

[ENDS AT 19:28]