Problem 15 Easy Difficulty

Oil leaked from a tank at a rate of $ r(t) $ liters per hour. The rate decreased as time passed and values of the rate at two-hour time intervals are shown in the table. Find lower and upper estimates for the total amount of oil that leaked out.

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01:24

Frank L.

05:48

Robert D.

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Video Transcript

So in this example you're asked to find the lower and upper estimates of amounts the total amount of oil that has leaked out. So you need to find areas of representative rectangles. So I randomly just made a graph. Don't know if that's anything close to what you have, But let's just say at time zero there's 10 leaders And then to there's eight l and then so on and so forth. So to find the lower estimate, I need to make a rectangle, It goes up to 10 over and back down. The width of this rectangle is to the height is 10. I don't even do that. Go up to up to the graph down and over 24 up to the graph Over down to six, up to the graph over down to eight. So when I calculate this I'm going to do the widths of each of these rectangles is too. So I'm not going to write out every time and then I'm going to add together all the height of the rectangles except I'm not going to use this last little itty bitty bit. So then I'm going to add those up and I'm going to get in my example in about 58. The number of leaders that leaked out. Now when we do the upper Now I am starting here at eight, going to the graph and over, going to the graph over up to and over and over. So the wits are still too. And then the areas I'm going to use now all rights will be mm I'm sorry that it will be too 5, 6 and eight hopes and eggs got these backwards tonight. You can tell from the picture the black ones are actually below the line. So this actually would be by upper and this would be my lower.