00:01
Okay, so we're going to be taking the derivative of x squared minus 4x plus 5 and then taking the integral of that derivative.
00:08
And so let's go ahead and do that.
00:11
So let's take the derivative first and then i'm just going to plug that value into an integral and take the integral there.
00:17
And so the derivative of x squared minus 4x plus 5, you can say that's equal to the derivative of just x squared, minus 4 times the derivative, not the integral, the derivative of x, and then plus the derivative of 5.
00:39
And so the derivative of x squared, we bring down the 2, we minus 1 to the power, so we have 2x here.
00:45
The derivative of x is 1 times 4 is just 4, and then the derivative of any constant is equal to 0.
00:52
So our derivative here is just going to be 2x minus 4.
00:55
And so we're going to be taking the integral of this function to x minus four.
01:02
And what we're going to want to do is split this up into two times the integral of x minus four times the integral of dx.
01:10
And i just took out the constants and separated this into two separate integrals...