00:01
Alright, so we want to find, we have this area function, the fundamental theorem of calculus, and we can find these areas by looking at the graph.
00:09
So the first one, a of 2, i'm going from 0 to 2, it's this little region right here, which we're told is a quarter of a circle with a radius equal to 2.
00:20
Area of a circle is pi times the radius squared.
00:24
We only have a fourth of it, so we divide by 4, so this comes out to be pi.
00:29
Now, it is below the x -axis, so it is negative, so don't forget to make it negative because it's below the x -axis.
00:38
Alright, now, when we go all the way from 0 to 5, sorry about that, i sneezed, i didn't want to disrupt the video.
00:47
Alright, when i go from 0 to 5, that's going to take me all the way to right here, there's 5 right there.
00:55
Alright, well i just got to find the area of this red triangle, but don't forget, remember this part is part of what our formula is too, our a of x formula is, so i got to add the negative pi or subtract pi off.
01:12
So the area of that triangle, so the base is 3, the height is also 3, so base times height divided by 2, that comes out to be 4 .5...