00:01
They want this to, let's see, determine the area between the curves y is equal to x cubed and y is equals 3x plus 2.
00:10
This will be by their intersection.
00:13
And let's see.
00:15
It looks like the intersect at x cubed minus 3x minus 2 is equal to 0.
00:22
Let's see some roots for this.
00:28
They'll intersect at negative or negative 1 and 2.
00:38
Okay, so that'll be our integral.
00:40
Our interval for our definite integral and it looks like the line would be on top of that whole time makes sense because x cubed only eventually outpaces it on the right side of the plane then we'll have minus x cubed and dx so let's take our antiderivatives we'll have 3 over 2 x squared plus 2x minus x to the 4th over 4 evaluated at 2 and negative 1 and then see what we'll get.
01:16
We'll have 3 times 4 divided by 2, 3 times 2, which is just 6, then we plus 4, and then we minus, let's see, 16 over 4 is just 4, and then we subtract, let's see, plug negative 1 in, so 3 over 2 here, minus 2, minus 1 4.
01:44
We just cancel out...
