WEBVTT
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Okay, let's go ahead and do the calculation in
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this problem. We're asked to basically find the area
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under the curve. Okay? Using the midpoint rule
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. Now, the points are not given to you
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exactly. And we don't know what the exact function
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is. So the best that we can do here
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is to use our eyes to estimate the values.
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So each individual, what may have a slightly different
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opinion on what the values are, so the answer
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is could differ a little bit, but I'll do
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my best in order to help you solve these kind
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of problems. No, What I did was split
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the bottom into equal parts so that the bottom with
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is equal to one. And of course, the
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more, Uh um rectangles that you will have,
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the better the estimation is going to be. I
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used 66 rectangles simply because it was easy. Mhm
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. Now the first hike from 0 to 1.
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It's insignificant. When you plug in the height at
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0.5, it's nearly close to zero. I know
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that it's going to be positive, but I will
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just use zero. Okay, I indicated zero plus
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just to keep in mind that it's not exactly zero
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. Okay, the next height, I am going
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to use the height at 1.5, which in my
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eyes looked like it was the height of two.
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So because the base length is, one area of
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this rectangle is going to be a two. Similarly
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, the next point at 2.5, the height to
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me looked like it was a seven. The next
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point I used looked like it was the height of
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12. Similarly, because it's symmetric, the next
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point also looked like it ended up being 12.
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Keeping chart is 345 and when I plug in 5.5
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, the height seemed like it was around six,
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and that exhaust all of the rectangles that I have
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. So the area under the curve using the midpoint
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rule in my eyes it looked like it was going
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to be zero plus two plus seven plus 12 times
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two and a six, so that number adds up
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to 39. So if your answer is somewhere between
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I would say 38 to 41 then that is totally
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acceptable. In my opinion, I think the calculation
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is probably going to be an underestimate. So it's
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more likely that you will get 40 or 41 if
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you'd used more rectangles. Okay. And that is
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how you answer this question.