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Hello.
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Okay, for this question, i've gone ahead and set up a whiteboard so that it didn't take quite as much time to record the answer.
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We have a function, x squared plus 2x plus 5, and we're asked to use five rectangles, or n equal 5, and to cover the interval from 3 to 23.
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So that interval is 20 spaces wide, divided up amongst four rectangles equally, means that each rectangle is, going to be four units wide.
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And then we're asked to use the midpoint method.
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So the midpoint of each of those four unit intervals is exactly in the middle.
00:44
So from three to seven, the midpoint is five, and then nine, and then 13, and then 17, and then 21 for the largest rectangle.
00:53
So if we plug those midpoint values into the formula, five squared is 25 plus 10 for five times two is 35 plus 5 is 40 and you can do that for all five of the midpoints so the second midpoint has a value of 104 the third midpoint has a value of 200 the fourth midpoint has a value of 328 and the last midpoint 21 squared plus 21 times 2 plus 5 gives you 488 now using the midpoint rhyme and sum mrs the first the first rectangle has a height of 40 times a width of 4.
01:38
The second one is 104 times 4 and so on...