00:01
Okay, in this problem, we're given that the integral from 1 to 3 of f of x dx equals 4.
00:07
And then we're given that the integral from 1 to 3 of g of x of dx equals 2.
00:12
And so what we have here is the integral of 1, from 1 to 3 of 2 times f of x, and then plus 5 times g of x, and then all of that dx.
00:26
So we have two main things that we need to remember.
00:30
And one of those is the constant multiple rule, and then the other is the sum difference rule.
00:35
So essentially what that means is that we can split these things apart into two different integrals.
00:42
We'll have 2 times the integral of 1, from 1 to 3 of f of x, and then plus 5 times the integral from 1 to 3 of g of x.
00:54
Right? now, this is going to be easy.
00:56
Our problem tells us what these things equal...