WEBVTT
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All right. We've got a question here where we're
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giving a table of values and we want to estimate
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the Integral from 3- 9. The function of
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X With respect to X. And we're gonna use
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three equals sub intervals. And we want to calculate
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for a the right The the left hand points and
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see the mid points. And then finally, if
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it is a function is known to be an increase
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in function to say whether you're estimates or less Then
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operator than the exact value. Alright. So to
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start off a part a, What we're doing is
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we know we have that three sub inter rules 3
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2579. And we're What we're asked to do is
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use your right endpoints for part a. So to
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begin, we know we're going to have three sub
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intervals. So the way that we would calculate for
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our change in X is you take your largest value
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within that interval And you subtract us lowest value within
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that Um interval. And then you divided by your
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southern rules that was given to us as 3.
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And you get to as your change in X.
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Okay. And then finally the way that you saw
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for your essentially your dream and some on the right
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end is you take your change in X which is
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two and then you multiply by the function of X
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. When you are functional X one was the function
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of except to What's the function of except Because we
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have three sub animals. All right. So you
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start off by saying, well what would be your
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X sub one? Your X one would fall on
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the the first Sub in a role. Excuse me
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, let me let me reiterate that to be a
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little quicker. So you have your your range of
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sub intervals we're told or three. Right. So
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you would have This being your one in some interval
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, this being your second interval and that's being a
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right, that is an equal space between three and
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nine. And then you have created a 3 subgroups
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. Okay, so whenever you're asked to solve for
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your Right and points, you take your first interval
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and choose the value on the right end. If
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you can see that our um interval, the first
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intervals from 3 to 5, second intervals from 5
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to 95 to seven and then seven and nine.
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So you would choose the value on the right hand
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side. So you would say well your ex a
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one in five then we know that X when x
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one is five, then you have a negative six
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. Yeah, The X up to it's 0.3 Excuse
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me. Except to would be at seven because that's
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the right end on your second sub interval And that
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is when the function of that's easy, quick to
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point out, Okay, and then your exit three
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is nine because that is the right endpoint on your
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third interval and that is when the function that's at
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one point. All right. So you're basically gonna
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be left with a final answer which is 4.2,
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alright, for part B were asked to the same
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thing, but this time on the left end points
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you take your same intervals and your instead of X
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of one being um five, you really would start
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off by saying except zero except one and exit to
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Basically what you're doing is you're choosing the left endpoint
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On your interval, which here would be three.
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We know when X is equal to three, we
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have a negative 3.4 In the left endpoint on her
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second sub in a rule It's gonna be when you
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have five and that's at negative.6. Finally,
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the left endpoint on your third. Some interval here
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is when X is equal to seven and that is
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point now. Okay. Your final answer will come
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out to be-6.2. All right. Finally for
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port, see taking your um Mid points of your
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intervals, you can see the midpoint would be between
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three and five which is four. We know an
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exit sequence of four. You have a negative 2.1
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If your second sub interval is between five and seven
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, so the midpoint would be at six and that's
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.3. Finally in the third sub interval value in
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the middle here is the main point is at X
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is equal to eight, which would be the function
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that's equal to 1.4. All right. So then
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when you go ahead and multiply orders across your left
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with a point negative 0.8. Alright. And those
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will be all of your final answers there. I
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hope that clarifies the question. Thank you so much
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for watching.