00:01
Use the fundamental theorem of calculus to find the area under the curve of negative x squared plus 9x between 3 and 7.
00:08
So we first need to do the integration.
00:11
So i'm going to come over here and do the integration of negative x squared from 3 to 7 plus the integration of 9x from 3 to 7.
00:24
So what we need to do is integrate negative x from 3 to 7.
00:30
X squared.
00:31
So it's going to be negative.
00:32
We increase our exponent by one and then give it the denominator of 2 plus 1.
00:40
So that's going to be negative x cubed over 3, which we will evaluate from 3 to 7.
00:48
Then for 9x dx, we're going to say that'll be 9x squared over 2, which we will again say plus 9x dx, we're going to say that would be 9x squared over 2, which we will again say plus 9x squared.
01:00
Over 2, evaluated from 3 to 7.
01:04
So we're going to come over here, put on the top.
01:08
I'm going to say negative 7 cubed over 3 minus negative 3 cubed over 3.
01:22
Then we're going to say plus 9 times 7 squared over 2.
01:32
Minus 9 times 3 squared over 2.
01:37
So this is the evaluation of the first interval...