00:01
Hi there, so for this problem, we are told that if the marginal revenue is given and that it is minus 12, this divided by 4 times x plus 15 and that to the 3 plus 25 and the revenue at 0 is 0, we need to find the revenue function.
00:26
So for this, what we need to do to find the revenue function is to take the integral of the marginal revenue.
00:32
Because remember that the marginal revenue is just the derivative of the revenue function.
00:38
Now we substitute that in here, so that will be minus 12 divided by 4 times x plus 15, and that to the 3 plus 25 is integrated over x.
00:53
Once we have this, we know that the integral of this term is right away just 25 times x, and we will have the derivative of this so we're gonna set that u is equal to 4 times x plus 15 so that will give us that the differential in u is just 4 times the differential in x so then we now will have that this integral becomes the differential in x divided by the differential in u divided by 40 is equal to the differential in x so we will have minus 12 divided by 4 which is minus 3 so that will give us minus 3 the integral of the differential in u divided by u to the 3 then this plus 25 already we know that that is x.
01:48
Okay so the integral of something like this we can write it as as well as just u, elevated to minus 3...