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Graph of f(r) is shown above: Using the geometry a) k" f)dy 1186) f(c) dx2K f() dr45d) L f(c) dx( 6f(c) dxAnswers Attempt 3 0f 3...

Question

Graph of f(r) is shown above: Using the geometry a) k" f)dy 1186) f(c) dx2K f() dr45d) L f(c) dx( 6f(c) dxAnswers Attempt 3 0f 3

graph of f(r) is shown above: Using the geometry a) k" f)dy 118 6) f(c) dx 2 K f() dr 45 d) L f(c) dx ( 6f(c) dx Answers Attempt 3 0f 3



Answers

The graph of $g$ is shown. Estimate $\int_{-3}^{3} g(x) d x$ with six subintervals using (a) right endpoints, (b) left endpoints, and (c) midpoints.

With. Now knowing what your graph is, the best I can do is give you an idea of how to solve this. You need to remember that integration is just Area. So if I'm asked to find the interval from 0-2 on my graph market off and look at what it is. In this case it's a triangle. Remember the area of the triangle is base times height divided by two. So the bases to the height is too and two times two divided by two or one half the base times height is to. So this area here is two units. Then the next thing you're asked Is the integral from 0 to 5. So now I'm gonna come over to five now I already know it's too so I've already got that part done too. And now I look and see, okay well this is a rectangle in the area of a rectangle is base so it's 123 units times the height. It's also two units long, so two plus six. So this would be six And so the area from 0 to 5 is eight. And then you're asked to find The interval from 5 to 7. So looking at my graph, make them a little dash here. I see I have a trapezoid and a trapezoid. I need to Add the parent length of the parallel size together. So this goes up to white four. So this sites four. So I'm going to add the parallel sides together. Multiply that by This width here which is two units and then take a half, So 1/2 times six times 2. So this particular in the role, This part of it would be six units long. So from 5 to 7 it would be six. And then finally you're asked to find the area From zero all the way tonight. So I already know I have two plus six plus another six. Sorry you have 14 units. Now I look at this last little portion and see it's also a triangle basis to height is for so base times height, 1/2 base times site is going to give me four. It's going to add another four. So the total area would be 18 units. So you need to break your picture up into geometric figures. Um if it's a circle you'll use pi r squared. But if it's a triangle or rectangle or a trapezoid, you can use your geometry formulas.

Okay, let's start with F of X and let's find some of its features. So because of before we know the amplitude is going to be four. So from a height of zero will go up to a maximum of four and down to a minimum. Look negative for And because we have a B value of pie in here, we're going to find the period by taking two pi divided by B so to pie divided by pi is too. So the period is two. That's the width of one cycle. So what I'm going to do is take the width of two and divide it into four equal chunks. So there's one and then 1/2 and then 1.5. We'll do that on the other side as well for equal chunks. Okay, so now let's draw f of X. So we're going to start at 00 and then we go up to the maximum of four back to the middle of zero, down to the minimum of negative four and back to the middle. And so there's one complete cycle and were asked to draw to full periods. So let's draw this on the other side as well. So here we are, the middle down to the minimum, back to the middle, up to the maximum and back to the middle. So this gives us f of X now for G. We're going to do this in blue and notice. The only change to the equation is minus three. That means what we're going to do is take f of X and shift it down three units. Now I like to think of these graphs is having a mid line. So the midline for F of X was just the line Y equals zero and the midline for G of X. Because we're shifting everything down, three is going to be the line y equals negative three. So what's going to happen is we're going to be at our midline here, and then we're going to go up to a maximum for units hire that will be up at a height of one. Then we'll go back to the middle and we'll go down to a minimum. Four units lower will be at a height of negative seven and then back to the middle. And there's one complete cycle of G and then we'll do the same on the other side. So we're at the minimum or at the middle will go down to the minimum at a height of negative. Seven will go back to the middle, up to the maximum at a height of one and then back to the middle. And there we have G.

We have Problem number three in which it is given that it is given that the e f and G f that is D E F and G f are the mid segments. Okay, Now we have to find the coordinates of the point D e and F d e and F. Now, if you look at the graph, we can find the co ordinate off a two weeks minus five. Comma two minus five karma to coordinate or be corn It off be is one comma minus two and cornered off. See is coordinator of C is minus one minus two minus three. Call minus six minus six. So coordinate of day will be corner of they will beta. Uh, we can find out from figure. Also corner of D seems to be 1234 Okay, since this is the midpoint in the is the midpoint of N. C. So we can find the corners. Fifth midpoint formula minus five, minus three by two and two minus six by two. So coordinate of d will become minus four and minus two. Okay, so this is the coordinator of D. Coordinates off Evil Be okay. He's the midpoint. off and be the corner off. Evil B minus five plus one by to come A to minus two by two. That is minus five plus one. That in minus four by two minus two comma zero. So this is the corner coffee. Okay. Cornered off F if is the midpoint off after the midpoint of B and C so minus three plus one by two comma minus two minus six by two. Yeah, so f cognitive f will be minus one comma minus four. Okay, so these are the coordinates of D, E and F. Thank you so much.

Because if we're this problem, because I'm plugging in 12 and three for acts, I consider each road to be what, up again for acts. So we'll get him one on one. Squared is one are coefficients would just be 111 Plugging into my coefficients for A B and C would be 4 to 1, and plugging in three will be 931 sense of my inverse matrix. For this, it's gonna be equal. Teoh 0.5 negative 10 point pyre. We're gonna have negative 2.5, uh, four and negative. 1.5. We're gonna have three negative three and one. Okay, So for part A, we're gonna have a inverse at times R K values. Okay, values for part air. Negative to one in six. Okay. And so my A, B and C values will be in order from top to bottom we're gonna get and a body of negative three B value of zero and see value of one. Okay, So for part B were and do the same thing. We're gonna change our K values to 43 and negative too, can't updating. There's it's gonna give us an ABC value of one five and negative too. Okay. And then part C. We're changing those K values, too. Eight negative. Five and four. It's a changing those. We're gonna have eight five, negative four. Okay, so our ABC values will leave five, six and negative three. Okay. And using these three points, this is pretty much exactly how quadratic regression would work if you're using three points. So this is also what quadratic regression and a calculator would give you Okay, for A B and C So again A B and C from top to bottom. Thank you very much.


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