 In this video, we provide the solution to question number seven for the practice final exam for math 1210 We're given a table to represent a function f of x where the first row of the table is the domain of f And then the second row of the table is the corresponding output of those values So for example f of 10 is negative 12 f of 22 is 1 f of 30 is 8 in that manner So using this table as our definition of x we need to approximate the definite integral From 14 to 26 of f of x dx and we're going to approximate this using r3 Which as a reminder r3 is the right end points with three subdivisions So let's look at the interval we're going for so we are going for the interval 14 to 26 All right, so here's 14 on the left. Here's 26 here on the right Because we're using r3 for this one that means n equals 3 which tells us our delta x is going to equal 26 minus 14 over 3 For which when we do the arithmetic there, we're going to get 12 over 3 that is we get a delta x of 4 so there's gonna be four steps between each of those places and so if we take four steps from 14 We're going to get 18 if we take four more steps we get to 22 and we take four more steps We're going to get 26 so in terms of our number line this right here is x 0 x 1 x 2 and x 3 If we're using the right endpoint rule to approximate this We need to figure out what is happening at x 1 at x 2 and x 3 therefore our 3 is going to equal delta x times f of x 1 plus f of x 2 Plus f of x 3 That's what we get for our 3 so let's plug in these values that we now know we've computed delta x Which is equal to 4 f of x 1 if we look at the table is a negative 2 f of x 2 is a 1 And f of x 3 is going to be 3 itself So Let's see what happens here 1 and 3 together as 4 minus 2 is going to be 2 So we end up 4 times 2 which is going to be 8 And so we see that the correct answer would then be D Which is the r3 approximation of the area under this function