All right, We've got a question here that is describing a testing of a new drug on it is tested. Um, at 10 minute intervals, the average concentration CFTR showing the table teas and measured in minutes sees measured in micrograms over milliliters. And we want to use the midpoint rule to determine integral from 0 to 100. See, of T dft. Okay, When we use the midpoint rule, we would take the Siri's eyes equal to one, and and we would have, um, see if t I multiplied by change and teeth. This is the midpoint rule here, and our n here is gonna be equal to 10. Okay, If we look at our table, we could see that we have intervals. I'm sorry. Readings collected at 0 10 2030 minutes. So r n will be 10 as it's changing 10 each time and then are changing t that actually will not be equal to 10. That's what that's what it looks like. The logical answer would be, but we have to understand how the midpoint rule works. We have a set of values from 0 to 100 and we're talking about midpoint bull. Since we have 10 intervals. We're going to need to now split these into five intervals. Would say 0 to 20. You wrote to I'm sorry. 20 to 40. 40 to 60. 60 to 80. And finally 80. 100. Okay, we have to consider these five intervals. When we're talking about midpoint rule, we're essentially splitting the amount of controls in half. Okay? And we're looking for is the midpoint of each of our five intervals. Yeah. Now here we can see that if the midpoint between zero and 20 would be 10, 20 and 40 would be 30 30 and 60 would be 50 70 you know. Okay, so are changing t here. Okay. Actually going to be equal 2 20. Good. We're saying it's changing. Went to okay. That's when we're you wanna make sure we do that correctly when we're solving for the midpoint. Well, okay, now, let's go ahead and bring this Siri's down. We know our and we've already calculated for we said that's gonna be equal to 10. Have I equals one. You have our sea of tea sub by Onda. That will be also these in, but we go ahead first, right out or change of tea won t Now let's go ahead and begin filling in thes values here. So now this is where we're gonna say. All right, We need Thio. Find the we're going to need to collect some of the mid points. Some of the mid points would be C one times t see, one time is 30 50 70 and 90. Okay, so what is this value here? See, when time it's 10, we're gonna add that to 30. Gonna add that you see a 50. Okay, I'm gonna add that to see a 70 and finally, we're gonna add that to see him. Okay. Now, when we go ahead and solve this out Excuse me. Um, you know, see, of 10 is 1.3. Also, one more clarification. Um, I want to write it out properly, So imagine it's gonna be a Siri's mhm, but this equals to this. Hey, this here. Sorry. This whole series here is equal. Okay, Now let's go and start filling in these values. See, when time is 10 is 1.3. Okay. See if 30 is 2.2. See if 50 is 25 plus, see if 70 or just 2.3. Let's see of 90 just 1.6. Okay. And when you add all these up together, it comes out to 9.9. Multiplied by 20 is gonna be equal to 198. We're told that this is in micrograms. Formularies multiplied by time, minutes. And so this will be our final answer here. And we can say that this is our final answer for when we use the midpoint rule to estimate the integral from 0 to 100 for function, See of tea. With respect to time, I hope that clarifies the question. Thank you for watching.