approximate-the-value-of-each-of-the-given-integrals-by-use-of-simpsons-rule-using-the-given-valu-18

Question

Approximate the value of each of the given integrals by use of Simpson's rule, using the given values of $n$. Exercises $8-10$ are the same as Exercises $10-12$ of Section 25.5
$$\int_{0}^{2.4} \frac{d x}{(4+\sqrt{x})^{3 / 2}}, n=8$$

Gideon Idumah · Accepted Answer

I first find the exact value off this integral, integral from zur. So deeds off Cuba&#x27;s off x dx. This is just called. So Cuba&#x27;s off exit exit exit E one of the three if I integrated, have one of the three most one divided by one of the three coast warn from zero through its if you plug this into the calculator. So you off, um three over four x to the forward three under in suits. AIDS Which is it called? So three over four 16 which is a call to solve. Well, he&#x27;s intra preserved our rule in this case we have that end is 1/4 of its So my daughter Hex, which is a ghost o b minus stay over end by these aids My 80 that&#x27;s it&#x27;s over AIDS, which is across the warm. Then this gives them a X zero is zero x one of the zero plus one, which is one. My ex too will be one plus one, which is to my ex three will be three and so on expo before and then x seven, maybe 1/4 to 7 and then ex aides of you gods who it&#x27;s So trump is it ever Records be minus a over. So end my B minus over end is one. Then develop. I&#x27;d sue. That&#x27;s one of the two multiplied by my f of x zero is cube root of zero plus sue my f of x one of the Cubans of one close sue Cubans off too, plus two Cubans off three plus to Cuba to four plus two Most blood I. Q. Bert off five Lost soo wants Bye bye, Q broods off Seeks plus sue moments played by Cubans off seven plus than Cuba it off AIDS. We don&#x27;t put it so the skim it off AIDS When blood isn&#x27;t a cock a little, you have 11.7296 Why is this Simpsons rule in this case? We have B minus eight over three N, which is my B minus over and his Wome divided by three. That&#x27;s one over 30 then f of x one. Kim birds off zero plus four children&#x27;s off one close to Cuba It off Sue blows four Cubans off 30 Close Sue que brutal full them box of four again Cubans off five clothes. So Cuba it off six Clause four. Cuba it off seven and loss Cambridge off AIDS if you plug it into a complimentary off in everyone points 8632

Shuyang Fu · Answer

Hi, you guys. This problem is to use the traps oId a rule in Simpson&#x27;s rule to approximate the integral for function square root off X from 4 to 9. So here the B the right end point off, the interval is nigh and the a the left endpoint off the interval is four and the in the number off sub intervals is eight. So the lens off the sub interval is B minus a over in that is nine minus four over eight, which is five over eight. So we need to divide the interval from five from four to NYU to eight parts evenly and each parts. We&#x27;ll have the length five over eight. Okay, so the first note is X not the second note x one. It&#x27;s four plus 5/8 that these 37 start 37 over eight. The next is 37 plus four over plus five over eight. That is 21 before, and then 47 overheat. And then 26 over four or further over two and then 57 over eight and then 31 over four and then 67 over eight. The lust Is that the nine. Okay, so we can mark itch note by X not x one x two up to x eight. Okay, so we can use the chaps or the rule now the integral from four tonight For the square roots X is approximately equal to ni over four over two times in which is eight times the function value. It&#x27;s the first note with question toe one. It was one times square roots off four plus two times the function value at the second note. Further seven over eight plus two times square root off thirds load plus two times square with off four snowed and then to Times Square, which off X four and then to Times Square roots off extra five and then two times square root off X six and then to Times Square root off X seven. Then for the last term, F off exit decryption is the one, so it&#x27;s one time square it off tonight by using the calculator. This number is round 12 point 6640 Okay, so next we can use the same since rule. Okay, so steal the same into grow. It&#x27;s B minus over three n. So it&#x27;s three times eight in the denominator and then one times square root off four plus four. Because the coefficient in The Simpsons rule for the second term is for so it&#x27;s four times square with off 37 over eight press two for the next corporations and then four again for the seven over eight and then to again, okay, for two for two or three nativity for the coefficient. So the function value are the same as the trap is always the rule, but the coefficient are different. Okay? And for the last two term coefficient is the one. Okay. By using the calculator, this is approximately equal to wealth. 0.6667 Okay. And the last thing is, calculates the exact value for this Integral. This is not hard, because this is just a power function for these power function. Square root of X. We can re vita it to X to the power. What? Hef. So the anti derivative will be one plus 1/2 didn&#x27;t nominate her into the X Times one plus to the one plus 1/2 in the new Marie either. So this is 2/3 X to the three halfs. You&#x27;ve had it it for and nine. Okay, so it&#x27;s 2/3 9 to the three halfs, minus 2/3. Four to the three halfs. That is equal to, um, 12.6667 approximately. Okay. So we can see the same percent. The rule is closer to the exact value. So it seems that the rule it&#x27;s more accurate than the chapel. Oi, The room. You know this Providence?

Angela Guo · Answer

to approximate this into girl. Using the trip is little rule we need to fill in the table on the left first. So for this question, our Delta X, which is equal to be minus a over end iss three over four. So this means our ex, not which is our A zero. And our ex one is going to meet a post three over four LP field before next one&#x27;s three over two, lying over four and finally free and f of X I we will just plug in our Ex I into our function, which is two x cubed plus one. So that gives us one denying over 32 31 over four, 761 over 32 and 55. So now with these valleys, we can use the the formula for trappers Little rule, which is written up here and read So that says into Rome. 0 to 3 of two x cubed plus one D x can be approximated by B minus C over and which is three over four and that&#x27;s multiplied by, huh? One plus with denying over 32 31 over four What 761 over 32 and was half of bye. So if we put that into a calculator, we will get that is equal to 1473 all over 32 for approximately 46.3 So now Part B, we do the same thing. But this time we&#x27;re using some stones rule, which is this formula written here in blue. And since those rule says then two girl from 0 to 3. Two x cubed plus when D X can be approximated by United, say over three on Well, that is three over 12. Multiply that by one plus war denying over 32. That&#x27;s two times 30 of one over floor, plus four times 7 61 over 32 and plus 55. And if we put that into a calculator, we will end up with 87 over too, or 43 0.5. No part C wants us to find the exact value. So which means we need toe solve this definite integral. So the anti derivative of to execute is going to be like the power for and in the closet in front. We&#x27;ll have to be 1/2 and then, um then he curative of one is just X and that&#x27;s evaluated from 0 to 3. So this is just half Ah, you to the power for plus three minus. If we putting zero, both terms will be zero. So this is 81 over two plus three, which is six over, too, which means our answer will be 87 over too. Or that&#x27;s just 43 25.

Angela Guo · Answer

were asked Approximate Doesn&#x27;t his role here with the trapezoidal cool. So before we do that, you need to fill out the table on the right side of the table on the left. So are Delta X ISS being minus a over, and so, in this question, are a is negative. One R B is three. In the end, it&#x27;s four were dealt. Eggs is just one. That means we will start a negative fine. And we go up by one. There are 123 and I was excited. For each of these excise will be one over two three over five, really before one and hurry over to. Do you find these values by just putting your ex I into the back. Such is here. So now, with all these values, we can put them into our formula, for the trap is little. Well, part ay says integral. From 1 to 3 of three over five minus X, the X can be approximated by be minus a over end, which was calculated up here. That&#x27;s just one times that&#x27;s half time us through over Size was three over for plus one, and the last term is half of that so half of three over two. And if you plugged in and your calculator, you&#x27;ll get this is 67 over 20 hate Now Part B. We do the same thing, but this time you seem so as well. So that says into little from negative 123 of free over five minus X yeah, can be approximated by be minus a over Fri end will be Mine is a S 43 times on a 12 and that&#x27;s times what have plus four times free over five plus two times three over four, four times one last 13 over two. Well, if you put this injury calculator, you&#x27;ll get it is equal to 33 over in the last part. Pricey. Or ask the justice I await the integral No, that&#x27;s from negative. 123 five minus x d. X. So the three on top is just a constant, which means they can actually just pull that out. That&#x27;s three times integral of negative 123 of one over five, minus X d x and the anti derivative of won over five minus X is just why five minus X, but because they&#x27;re the negative. We have to account for that. Which means they&#x27;re gonna multiply thy negative one. And that&#x27;s a relative from negative one three. We&#x27;ll just move the negative, the front. So that&#x27;s negative. Three. And that would be one of five minus three. So that&#x27;s long, too. Line us on a five minus negative one of Lawn six and using our log rule. We know that one of two minus line of sixes just long of 1/3 and using the other law girl that tells us we can put this constant up as a power that&#x27;s long of won over. Three. The power of Negative three, which is just one of 27. So that&#x27;s your final answer. Um, if you want, you can put it into your calculator. That is just awfully. Three point 296

Angela Guo · Answer

to approximate this integral here. Using the trap is little rule. We need to use this formal written up here in red. But before we can do that, we need to find the values to plug in, which means we need to fill out this table here on the left. So let&#x27;s start with calculating or don&#x27;t tax. So Delta X is equal to be minus a over end when this case or be a four way is to, and our and his boy, that&#x27;s two over four, which is when 1/2 what this tells us. Rx night, which is a is going to be choose and the next Excite is going to be true. Plus 1/2 Bible, too three, seven over too. And finally for So now that we have the excise cleaning to plug in or excise into our f of X, which is the one over X cube so that we can find our effort backside, plug in to we will get won over eight. This will be eight over 1 to 5 will be won over 27 eight over three for three and one over 64. So now that we have all the valleys when you can plug these numbers into a song left So which stand integral, Come to the whore of one over X Cube d X can be approximated e do you mind to say over and which we&#x27;ve already calculated to 1/2 times? I hope 1/2 of one over eight plus eight over 1 to 5 was won over 27 US eight over three for three and plus half of one over 64. So if we put this, but this is, your calculator will get approximately 0.0 973 You know, part B. We do the same thing, but this time you use Simpson&#x27;s well. No sense of his rule says Integral. From through the floor of one over your beauty, X can be a fascinated as B minus eight over three end. So that is too over 12 and that&#x27;s multiplied by one over eight plus four times eight over 1 to 5 waas two times won over 27 plus more over eight times before three Life won over 64 and was we plug that into account the waiter. We&#x27;ll get approximately a 0.0 nine boys zeros. And now Part C wants us to find the exact value by valuing ring to them both in general, from 2 to 4 of x one over X Q Deac Buttery, right, that an exponential form. Is that a X appellate negative three. The ex, so anti derivative of that. We know the power has to be negative too, right? Once we take the dirt of this, we&#x27;ll have a negative two in front. Which means we need to cancel that out with a naked of house. And that&#x27;s gonna be a violator from 2 to 4. But this is going to be negative 1/2 for the power of negative, too. Bush is just one over 16. Two Little power of negative, too. That is just one over four, and this is AL awaits out to be three over 32 which is equal to 0.0 lying 375

Problem

Approximate the values of the integrals defined b…

Problem 12 Easy Difficulty

Approximate the value of each of the given integrals by use of Simpson's rule, using the given values of $n$. Exercises $8-10$ are the same as Exercises $10-12$ of Section 25.5
$$\int_{0}^{2.4} \frac{d x}{(4+\sqrt{x})^{3 / 2}}, n=8$$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Grace H.

Heather Z.

Kristen K.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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Basic Technical Mathematics with Calculus

Grace H.

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

Grace H.

Heather Z.

Kristen K.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus