00:01
So the way i would approach this problem is start with that integral from one to four.
00:04
Oops.
00:06
It's one to five of negative four x squared dx.
00:14
And just manipulate this equation first by moving that constant in front.
00:20
It doesn't matter if you multiply a function by negative four and then that integral of it or do the integral of the function and then multiply by negative four.
00:29
You'll get the same answer.
00:30
You'll still get the same area under the curve.
00:33
Curve.
00:34
The next thing i would do, though, is so now i have that negative 4, i would actually split up the integral from 1 to 5 to be from 1 to 4 x squared dx, and then plus.
00:48
And now i do need to put parentheses around here because the order that you do things is negative 4 is multiplied by the entire quantity, 4 to 5 of x squared dx.
01:00
And i should also point out that this is true if we're going from 1 to 5, as long as this number is the same.
01:07
It doesn't have to be 4, but the reason why i'm using 4 in this problem is because when you read the directions, we know the quantity of this, the integral from 1 to 4 of x squared dx is equal to 21, and they tell you from 4 to 5, it is 61 thirds.
01:31
Now, you might have a teacher that lets you use a calculator.
01:35
Otherwise, you might need to change this to be the same denominator...