5

Y= f(x)=sin.xGraph vi10}y=fr)-4r-12-2 -1 24 5 6 7 8 9 1055 (18)-10 Graph v.13 . Use Graphs v and vi on this page to find the value of each definite integral.fsin x...

Question

Y= f(x)=sin.xGraph vi10}y=fr)-4r-12-2 -1 24 5 6 7 8 9 1055 (18)-10 Graph v.13 . Use Graphs v and vi on this page to find the value of each definite integral.fsin x dxJustify the answer using complete sentences

y= f(x)=sin.x Graph vi 10} y=fr)-4r-12 -2 - 1 2 4 5 6 7 8 9 10 55 (18) -10 Graph v. 13 . Use Graphs v and vi on this page to find the value of each definite integral. f sin x dx Justify the answer using complete sentences



Answers

Match the graph with one of the following possible values for the integral $\int_{0}^{5} f(x) d x.$ I. -10.4 II. -2.1 III. 5.2 IV. 10.4 (Check your book to see graph)

Hi there. So a number of 15 here we have this graph for F, so we just need to do a quick estimate of the, uh, area the interval between zero and five and see which of the choices it's closest to. So we won't even look at the choices yet. Let's just try to get an estimate for ourselves. Well, the inner girl here from 0 to 2. Let's do that first. Since it's all positive, it's this shape right there. It's about a triangle, I'd say Israel fi triangular. It's about a triangle at the base of two and a height of 20 in such a triangle. Obviously, it's 1/2 based time site, 1/2 2 times 20. So area would give us about 20 there. And now let's get the area from 2 to 5 right away. We can tell it's going to be negative, since it's all beneath the X axis ending. And if you think of it as roughly a triangle, it would have a base of three. Since that's the distance from 2 to 5. And the height, I'd say is about negative or hide. Is Neha as a high? This is 10 10 10 units beneath the X axis. So this is all very approximate. Three times 10 is 30 half of that would be about 15. And so if we want, then the overall integral from 0 to 5, it should be about our 1st 1 from 0 to 2. Plus, remember, our 2nd 1 is negative since it's beneath. The ex ex ists were subtracting about 15 so we would expect Ah, something roughly around five and let his look at the choices. And the only one that's even close to this is Choice three, which is about 5.2. So that's the only one that makes sense and

Neither. Then this problem. We are going to try to estimate the definite Inter girl from 0 to 5 of our function f for this graph grown here for number 16. Um, now, this is just an estimate. So let's first look at this first part from 0 to 2 so we can see from 0 to 2 again. Just an estimate. Why don't we just try to make this into a triangle sort of shape, right? It's certainly not perfect, but it's something so it looks like the curve goes up to about five. So if we have a triangle which is of base to and of height five, well, the area of a two by five triangles, 1/2 times, two times five. So this is all approximate, of course, but I'd say about five units there announce us to the second part, which starts at two and goes to five. So this part beneath the X axis because it's beneath the X axis, certainly going to be negative. And once again, let's make a little triangle for ourselves, since this is a roughly triangular, so I don't know if it goes till, um, it's got a base of three and a height of Don't have nothing past five. I don't know what you want to call it. Six or seven. Call it six. Just two numbers even here. So three by six triangles, 18 half out of the nine. So then our estimate for the integral from 0 to 5 when we just have to combine our to inter girls that we did the loan five plus negative nine. It was about negative. For now, if you look at any of the choices, none of them are that close to negative for, but certainly the closest. Um, is choice three. I'm sorry. Choice, too. So choice to it was about negative 2.1. And it's certainly certainly the answer has to be negative. And it's definitely nowhere near negative. 10. Um so the only the closest estimate by far have to be choice, too. So that's how you do this

Neither. In this problem, we are asked to estimate the definite integral from 0 to 5 of F of X. If this is the graph of F given in number 17 eso, clearly it's positive. Thea the curve lies above the x X is so something positive. If we look at choices three and four. Three was 5.2 and for 10.4 it was one of these two since the these air, the only positive choices and just looking at what we have since this curve lives completely beneath the height of two and we're going from 0 to 5. Um, it's cooler. Clearly, well, less than 10. In fact, it's much less than 10 since 10 would be a two by five rectangle. So for you can tell his way too much. It does occupy roughly half the area it looks like of a two by five rectangle. So definitely for this one choice three

In this case, we have a definition. Take curable five d v. Not a limit of Dickerson from 49 So this can be written us. Why even take this in a four or nine Devi? Integration of TV is to be go to 9759 minutes. Work just called off. 55 Cisco contains five. In order to verify this, we will use a graphing calculator. So the one satisfied indignance nous from food from nine. The answer is 25.


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