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Homework # 12 Assigned 06-23 due 06-30 Chapra, Chapter 24Read Chapra 24.1 24.3Use finite difference with a step size of 5.0 to solve7 4-2-"+4=0 dx dx with the ...

Question

Homework # 12 Assigned 06-23 due 06-30 Chapra, Chapter 24Read Chapra 24.1 24.3Use finite difference with a step size of 5.0 to solve7 4-2-"+4=0 dx dx with the boundary conditions "(O) = 5 and "(20) = 8

Homework # 12 Assigned 06-23 due 06-30 Chapra, Chapter 24 Read Chapra 24.1 24.3 Use finite difference with a step size of 5.0 to solve 7 4-2-"+4=0 dx dx with the boundary conditions "(O) = 5 and "(20) = 8



Answers

Numerical Integration In Exercises $75-78$ , use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral. Let $n=4$ and round your answer to four decimal places. Use a graphing utility to verify your result.
$$
\int_{1}^{5} \frac{12}{x} d x
$$

Still discussing America integration. We have the function f of x f of X to be equal to laying off. Eight. This implies that B minus a be my next A is going to be six minus two, which is equal towards four, and we are seeing in. It's equal to four. So with America and situation, we want to look at the trapezoid. Seen the Simpson rule to solve for this Integra. So for the trapezoid trapezoid, we have M C vehicles. So we have B minus a, which is four divided by words to of words our and it's also going to four. Then I evaluate that's what they're for forward to, plus two f of three Bless two A 44 half of four plus 446 the last but and this is going to be equal to one over to If I evaluate this lean at this, a Leonard's too laying eggs at two. That gives me 0.6 931 plus two. If I valid, the eggs are three times to that also gives me soon, and it's one nice something to plus this is going to give me 2.77 to 6. Plus. So I have therefore five. Don't forget, There for five is to hear 5.5 glass f 56 That's we nearly made. So I have three 0.2 189 lads f of 6. 21.7. My one it's and this is going to give me five boys. Three, 368 Let's consider that of the Simpson room. So, for a Simpson group, what do I have? I have four. Three before then. I have her fourth, too. Last four f of three plus. Mm hmm. F of words for less. Uh huh. A 45 Yes. Therefore for six. Yeah. And this is going to and over three. Let's evaluate. If he evaluate this, if he evaluate each point, then this whole thing is going to give us write a finer answer. Play. So thank so just like we did for this part. So you know the value for this? You know the value for that as well, Then face, that's all. So if it's simplify, this is sick. With violence, too. Five points. 3632 for the America integration for with the trapezoid. I think there? 17. But if you use a calculator, then then speaker of two from 2 to 6 of length of eggs, the A s is going to be so equal, it's going to be equal to five. Mhm. Five points. 36 for three celery, right? It's hard to say that it's five. When. 364 To me, this is all we get if we use calculator.

So this questionnaire about being into girls and we're going to use our equations to thirty four in our rules and table five point six. So this integral concerned Teo five x t x. I know from my constant multiple rule that I can pull out Constance and pull it in front of my integral. So this is going to equal five times and a girl from zero to two of X T X and then from equation, too. I know what the General front of Exes is. Just gonna B b squared, minus a scared all over, too. And so I say, my B is to hear some two squared over two minus my A, which is zero squared. Number two. So that's just going to zero Two squares for four. Divided by two is two and then five times two is ten. That's my answer.

And so giving the Integra. So I have with Zika from 0 to 4 aids divided by its great plus for the X And I want to evaluate this integral to using the trapezoid a roux Fitz Let's look like the trapezoid LaRue, the trapezoid, aru, Zoraida, the trapezoidal we see in the area Oh, I into gra in single from a to B of f of x A is going to be a be my next a number two and then I evaluate the function afterwards Eggs nuts plus so f of x one Mhm Last two f of words x two plus two f of s three less if that's what it's for. Okay, so we know what b a s we know what a s. B. S four is what? Zero And we are told that our N is equal to four. So this implies that I have words This is going to give me 1/2. Let's evaluate this at zero. This is going to give us zero effort towards X one. So this is one. This is one You have to You have three in our words four here. So at one, I have words to two times words eight. Divided by five plus at two. The function that is going to be 16/8 plus three. What do I have? 24 Divided by 13. Then at four, I have words 32 provided by 20. Okay, so if you simplify, then you're going to get 6.2462 then for the Simpson rule. So let's look at that of the same thing through actual seven cents through it says I have words. Thanks. You guys going to give me my be my next? A Divided by three and f of words we evaluated effort. Zero less evaluate sides for if that's one efforts one. No plus, Yeah, mhm. We evaluate as FF efforts. Words, too. Then plus four. You value. It's different. Three. The U values the function as what for? Yeah, that we know already. So this is going to give us 1/3 for this. This is going to Cuba through plus four times. Words are eight divided by five plus four Last two, 24 04 two plus two, that's what. 16 Divided by eight. It's four f i three s words, etc. 24 divided by 13. Plus, With our efforts for which is 32 divided by 20 we simplify, and this gives us six points. 46 15 So using, uh, in America, integration of your trapezoid, a rule and your Simpson room, we can approximate our definite integral to. So this value for the trapezoid er and the Sims Simpson, you

Number 23. They asked us to use Simpson's room and equals 1 40 or used intuition future on a graphing calculator and approximate the feeling in jewels. I I think this is insane to use Simpson's rule with n equals 1 40 by hand, that doesn't make any sensible. Um, that's 140 terms that you would have to calculate by hand. I don't know. I didn't do the chapter on Simpson's ruled sadly so. I'm not sure how this book does it, but let's not do it by hand because that would be insane. That would take us, uh, hours literally. Um, instead, I'm just gonna use integration fusion. A graphing calculator. Um, this will be highly dependent Graphing calculator. You guys have a home instead? What I suggest is you used, um, Wolf friend Alfa so you can do a Google search for that is very and they're useful website for math and physics, and probably more. And so there's just like a search bar in it in which you can right pretty much anything, and it's gonna try to understand their the query you're giving it. It's It's very smart, so if you don't know that website I would strongly anchored you. Get up, Wilton. Alfa, You can do in two girls in there. So what I'm typing in Wolfram Alpha is Oh, I'm gonna use text for this one. So in the one fun offer, I'm simply typing integrate, uh, zero. And then you read Continue on the great 0.5 e to death. And it's your 0.5. I'm six. And then what you do is you can write. For example, from zero 35 you write this square in Roth and Martha, it's gonna give you the answer. It is that smart. And it's gonna also is gonna show you the integral that it's calculated into him more pretty form. So you can verify that it is the correct answer. I already can just check that. You asked it the correct question. Okay, So if I do this on Wolf, an offer for problem, eh? I get Zira. Um, that's right. No, that's That's from 25. Sorry. In this case, 23 for a I get one for B. I get two. And for see, I get it. So there's a d answers you should get as well. Um I am not true with the goal. They're running goal for this problem. Maybe you'd have to do number 24 which seems really did do it. But sadly in between for is not on my numerator assignments, so I will not be covering it. Andi will be moving on to Bum 25 which is very similar to this one.


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