00:01
Now in this example, we are going to use the fundamental theorem of calculus to evaluate this integral, which means we are going to do the integration of this function, 8x cubed minus 3x squared, and then plug into 2, and then subtract that by the integration of the function that has a negative 1 substituted in.
00:21
So first off, when we integrate this, we're going to increase the value of each exponent.
00:26
So in the first part, that exponent will turn into a first part.
00:30
And then we divide by that exponent.
00:33
And for the second piece, we will increase that exponent to a three, and then divide by that new exponent of three.
00:41
Now, each of these do simplify pretty nicely for us.
00:45
In the first part, we have 8 divided by 4, which is 2, x to the 4th.
00:50
And then the second part, we have 3 divided by 3, which is 1, which just leaves us with x cubed.
00:55
So the fundamental theorem of calculus says into that function, we can substitute a 2.
00:59
We can also substitute the negative 1, and then we are going to do the difference of those two things.
01:06
So when we sub in a 2, we will have 2 times 2 to the 4th minus 2 cubed.
01:15
And again, that was plugging in the 2 to that function, and we're going to subtract that by that same function with a negative 1 substituted in.
01:26
So if we substitute a negative 1 into that part, we would have 2, times negative 1 all to the 4th, decreased by negative 1 to the 3rd...