00:01
All right, so we have y equals 2x, just a diagonal line like this.
00:06
We also have x equals 5, and we also have y equals 6.
00:13
I guess i should have drawn a few things in here like this.
00:17
So what's important to this is, and we're with the x -axis, we're talking about this region.
00:23
So what's important is if y equals 6 right here, and we think about what the x value would be, you know, if we set 6 equal to 2x, then you divide the 2 over an x equals 3 would be your upper bound of that function to x dx.
00:42
That we need to add to it the integral from 3 to 5 of the upper function being 6 of dx.
00:53
So if you evaluate this integral, so this is part a, by the way, you add one to the exponent and divide by your new exponent, and that should make sense because the derivative of x squared is 2x.
01:03
And then this piece would be 6x going from 3 to 5 that you can plug in your bounds.
01:11
Well, 3 squared is 9, 0 squared is 0.
01:14
And then on this other one, 6 times 5 is 30 minus 6 times 3 is 18.
01:20
So we're looking at 9 plus 12...