00:01
For this problem, you're asked to find the area bounded by the two curves given.
00:05
So the way that we want to do this is by first, or essentially just finding the points of intersection between the two curves.
00:14
So we'd have 2x minus x squared must be equal to 2x minus 4.
00:19
So that will be the case when negative x squared equals negative 4.
00:24
Or when x squared equals positive 4, so that will be when x equals plus or minus 2.
00:31
I'll also note that in that region, we'll have that 2x minus x squared is greater than 2x minus 4.
00:40
So to find the area between the two curves, we'd find the integral from negative 2 up to positive 2 of 2x minus x squared minus 2x minus negative 4 turns 2 plus 4 dx.
00:56
So this then becomes integral from negative 2 to positive 2 of just 4 minus x squared dx.
01:06
She will then give us a result of 4x minus x cubed over 3, integrated from negative 2 up to positive 2.
01:15
So this will then give us 4 times 2, 8, minus 2 cubed, 8 over 3, minus 4 times negative 2, so minus negative 8, minus negative, pardon me, minus negative 8 cubed, or not 8 cube, pardon me, minus negative 8 over 3...
