00:01
In this question, we have been given that the rate of change of revenue for the sale of x calculator it is given as r dash of x equals to x plus 3 log of x plus 3.
00:16
We need to find the total revenue for the sale of first 13 calculator that is we have to find just r of 13.
00:24
Let us see how we are going to do this part here.
00:28
So, first of all, we try to get what is r of x.
00:34
So, we have to integrate this r dash of x dx.
00:37
So, this integral of x plus 3 log of x plus 3.
00:44
Let us see how we are going to do this.
00:46
So, we will apply integration by parts to solve this.
00:50
So, first function i will take it to be log of x plus 3 and this is my second function.
00:57
So, first times integral of second minus integral of derivative of first times integral of the second function, correct? then we take the whole of the integral.
01:12
So, this is equals to log of x plus 3 and we know that integral of x is x square by 2.
01:20
So, in place of x we have x plus 3.
01:23
So, x plus 3 square over 2, this will be minus 1 over 2 times...