approximate-the-value-of-each-of-the-given-integrals-by-use-of-the-trapezoidal-rule-using-the-giv-12

Question

Approximate the value of each of the given integrals by use of the trapezoidal rule, using the given value of $n.$
$$\int_{0}^{2} \sqrt{x^{3}+1} d x, n=4$$

K B · Accepted Answer

So in this Washington Masters, always undergoing using the trap is or a cool. So we know that it&#x27;s gonna be equal to be minus a over and which would be 0.4 months, zero over four. So is your point for before, you know, just want one time divided by two is 1/20 we&#x27;re gonna be using 1 28 times after zero plus two f was your wife. I trust you have 0.3 That was your one tube plus two after 0.3101 tent every time. That&#x27;s what are came, Darnell. Tax value is lust. You have 0.3 and then finally class just after a part for So now we can put all these values into our function. At the end, we multiplied by 1/20 for the story. Individually, we multiply by two after we got basically just fucking When we have here tour calculator, you get 0.219 That&#x27;s our final answer

K B · Answer

So this question we asked us all of using a trap is loyal. So we know that this is gonna be equal to be minus a over ad, which is the same. It&#x27;s 0.5 minus zero point whatever for that 0.4 over four, which is one attack. So we&#x27;re gonna be using one time over. To which 1/20? This is times at 0.1 plus two after the 0.2 us to have a zero point Greek. We see we&#x27;re adding 1/10 every time because that&#x27;s heart felt about you. Must you have 0.4 and finally we have our upper limit, which is your 0.5. So finally, plus f, it&#x27;s your plant pot. So now we basically were not everything we need. You can just plug it now this all but all this in your calculator and multiply 1/20 when we get our. Finally, there&#x27;s 1.624

Victoria Dollar · Answer

Okay, So for this problem, we have an equals for and f of X is going to equal to X to the third plus one. And we were working on an interval between zero and three. So what? The first thing I want to do is is I&#x27;m going to create my table. And so that way I can determine which x and ffx values I&#x27;m gonna be working with. So I&#x27;m gonna take my interval to figure out the increments on. I&#x27;m going to subtract the two and divide by my in, and this is going to give me 3/4. So I&#x27;m going to start off with zero, and I&#x27;m gonna add a 00.75 thio each increment until I get Thio three. So then, if I were to plug in X, these X values, I would get the, um, following f of X values and then 7.75 23.781 and 55. Okay, so these were the f of X values I&#x27;m going to be working with. So then what I&#x27;m going to do is I&#x27;m gonna be working with, um, the trapezoidal rule, and that&#x27;s going to be the formula of the change in X over to And then I have my first ffx plus two times the second one plus two times the third one and then two times the fourth one and then my last one is actually not gonna be multiplied by two. Just gonna be by itself. So then what I&#x27;m gonna do is about plug in my values. So we said that f the change in X is going to actually be 0.75 or 3/4. So then my first ffx value is one. My second one that I found was 1.844 My third one was 7.75 and then 23.781 And then my last one I had was 55. So then, if I were Thio, multiply and add everything inside the brackets. I would get 122.75 and then multiplied by 0.75 Divide by two will give me 46.313 Okay, so then the next thing we want to do is using Simpson&#x27;s rule. So Simpson&#x27;s rules somewhat similar to trap his idol, But with some minor differences. So that same change in X this time dividing it by three times f of X zero plus four times the second f of X, I have plus two times the third one plus four times the fourth one and then plus the last one. So I&#x27;m gonna have 0.7 5/3. And then I&#x27;m gonna plug in the values in the same fashion I did last time. So 1.844 plus two times 7.75 plus four times 23.78 one plus seven plus 55. So then, if I were to add and multiply everything in the brackets using order of operations, I&#x27;m going to end up getting 174 and then 0.75 divided by three is just 30.25 So this is going to be 43.5. Okay, So then to determine the actual value, we&#x27;re just going to apply the anti girl. So it&#x27;s from 3 to 0 of two x to the third plus one D X. So I&#x27;m going to have my two X to the fourth, Remember? I&#x27;m gonna add one to it. And then I want to take that forth and multiplied by the and by the reciprocal and then plus X from 3 to 0. So then this is going to give me one half X to the fourth plus X from 3 to 0. Three to the fourth. Power is going to be 81/2 plus three. And then, of course, both of thes have excellent, so it&#x27;s going to be minus zero. So then 81 halves plus three is going to be 87/2, or this is simply just going to be 43.5.

Victoria Dollar · Answer

Okay, So for this problem were given that n equals four our f of x equals two X to the third plus one, and this is gonna be on the interval from negative 1 to 2. So the first thing I want to go ahead and Dio is set up my table so I can determine my f of X values. And then I also need to figure out my increments in between these intervals. So what I&#x27;m gonna do is I&#x27;m gonna go ahead and take two and subtract negative one and divide by in, which is for so this is going to be 3/4 or 0.75 So I&#x27;m gonna go from negative one up 3/4 to negative 0.25 and then up 3/4 again, 2.5 and then up again and then up till we get to two. So then, if I plug in the X values, I&#x27;m going to get as follows. So 0.96 um, nine. 1.25 4.906 and 17. It looks like a huge jump, but it&#x27;s actually it. It kind of jumps a lot around a lot. So the first thing I want to do is I want to use the trapezoidal rule, so it&#x27;s going to be the change in X over to times f of x of zero plus two f of x one plus two f of x two plus two f of x three plus f of x four. So now I have to do is plug values in. So we already said the change on X is that 0.75 that we found earlier and then I have negative one plus two times 20.969 plus two times 1.25 plus two times 4.906 plus 17. So then, if I add everything inside the brackets and multiply everything based on the order of operations, I get that it&#x27;s 30.25 So then my final answers. 11 points. 3438 So now to use Simpson&#x27;s rule, it&#x27;s very, very similar. So it&#x27;s going to be S four equals the change in X over three. So then my do ffx not plus four f of x one plus two f of x two, plus four f of x three plus f of X four. So now I have to do is plug values in. So the change in X is going to be that 0.75 value we calculated over three. So then I&#x27;m going to have a negative one plus four times 40.969 plus two times 1.25 plus four times 4.906 plus 17. So then, um, 0.75 divided by three is just gonna be 30.25 And then if I multiply and add everything inside the brackets, um, I get 42. So then my final answer is 10.5. So then, if I were to actually go in and sulfur the integral so we get the integral from two to negative one or negative 1 to 2 of two x to the third plus one d X So then I can I&#x27;m gonna have X to the fourth with my two in front and then remember, I want to Duthie new exponents. Um inverse. Multiply to that and then plus x from two to negative one two times 1/4 is going to be one half x to the fourth plus x from two to negative one. So if I look at two so to to the fourth of 16. Half of 16 is eight plus two minus negative. Once the fourth will be one half eso. Yeah, negative. One to the fourth. Power will be positive. One times. One half is one half and then minus one. So this is gonna be 10 minus negative, one half, So we&#x27;re gonna have a double positive, so it&#x27;s gonna end up being 10.5.

K B · Answer

So in this question, were asked to use the Trappist little toe solve this interval. So we know we need Thio first, find B minus a over ad, which in this case is gonna be equal to 0.8 minus zero over four. So is your 40.8 before, which is just 0.2. You know, we have this value, so you know your point. You divided by two is one tax. We have 1/10 times now we&#x27;re gonna have is a zero plus 2/2 of zero plus 0.2. That&#x27;s just gonna be 0.2 plus two off of this bust. Your point. You start to half of 0.6 class, find the apples. You&#x27;re pregnant. So now we can just plug all these values in 00 point. Use your protection through when they multiply them by whatever number. Oh, sorry. I missed one. We need plus, um, two after was your 20.4 swell? It&#x27;s now we can just plug all these and finally the only box by about 1 10 So we got 0.655 is our final answer to this posture.

Problem

Approximate the value of each of the given integr…

Problem 10 Easy Difficulty

Approximate the value of each of the given integrals by use of the trapezoidal rule, using the given value of $n.$
$$\int_{0}^{2} \sqrt{x^{3}+1} d x, n=4$$

Answer

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Catherine R.

Anna Marie V.

Kayleah T.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

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Basic Technical Mathematics with Calculus

Catherine R.

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Precalculus Review - Intro

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Catherine R.

Anna Marie V.

Kayleah T.

Kristen K.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus