00:01
The question is being asked find the shaded regions.
00:04
So the first area, which is, so the area, which is equal to, so we have to just write the function or the integral in terms of x, the variable x.
00:17
So it is changing from 0 to 4 and the upper function, which is 5x, minus x squared and minus x.
00:25
The x, let's take the integral of this expression, which is 0 to 4, that should be negative x squared plus 4x.
00:34
The x.
00:36
So if i take the integral of this expression, which is negative x cubed over 3 and plus 2x squared, the interval is 0 and 4.
00:44
If you plug in the values, which is negative 64 over 3 and plus 32, that should be 32 over 3.
00:52
So this is the shaded region for the first question...