evaluate-the-given-definite-integrals-int_-3-2left3-x2-2right-sqrt32-x3-4-x1-d-x-3

Question

Evaluate the given definite integrals.
$$\int_{-3}^{-2}\left(3 x^{2}-2\right) \sqrt[3]{2 x^{3}-4 x+1} d x$$

Dwijendra Rao · Accepted Answer

elephants. We have to value that given definitely and giggles interviews and of monastery two months two three X. S. car managed to integration ALs to work school Monitor four x plus one over the X. So this can be integrated with the substitution this time will be substitute order placed by you. Bye. Differentiating it with this spoke to her. So there will be six off axis square minus or food. Do you accept question do you? So we called three actress Carmen is a group. The use of the question you were born to. Okay then asked the question Monastery Then you will be to ministry to the cover three months of four. I don&#x27;t want to sleep plus one So two and 2 months of 27. Let&#x27;s turn this month. Yeah. Yeah this will because two months of forgiven when agriculture managed to then you will be. Yeah. So this is because you go into -8. Listen Yes one This will be minus of 16 Plus eight because 1- of eight as 1 is- of seven. These are the new. Yeah. Yeah. Okay so this will because to integration of- of 41 3 minus seven U. to the power of one x 3 you&#x27;ll be please three ex communist 20 of the ex because to do you wear to do you want to? So this will be the first to move one upon to Money than 41 2 months of seven. So this is a cost to one will do. Mhm And do you smell this will leave money one plus three plus one That is four x 3 A bomb You can the power of four x 3.413. LTD minus 41 2 minus of seven. So this is your chance to in front of 12 into three a point four months of 7 to the power of four x 3 minus off 41 to the power of for Valtteri. Okay, So this may be because of three x 8 minus of seven to the power of four by three. So this is minus of 13.39. Okay, Manager of 1441 to the car. For what really matters of 1 41.376. All right. Mhm. Multiple with 3 4 years. So, this will be a cost to 47.995. So, this will be cost two months of 47 199 five. Sorry, this will be positive. This is um, was it? So these are the this is the answer. I hope you on the show. Thank you. Okay.

Ramzi Deek · Answer

So we got into girl of three X plus one over four minus X squared. Square root of four minus X squared DX. We&#x27;re gonna split this fraction into two. So integral of three X over square root of four minus X squared, plus one integral off one over square root of four, minus x squared. Uh, I&#x27;m gonna work with gonna label this as one and two gonna work with one first. So integral off three X over square root of four minus x squared. I will take you as four minus X squared. So do you. Over D X is minus two X. So do you over minus two works is DX Uh, Now let&#x27;s integrate. So that&#x27;s integral off. Just gonna put three outside times x over square root of a few times, do you over minus two X. So that&#x27;s equal to minus 3/2 into girl off you to the minus half Do you so integrating from there? So that&#x27;s minus 3/2 times you to the half divided by half, which is ah, same as multiplying by two. All right, so that&#x27;s minus three square root a few minus three square root of you, which is also minus three times scored a four minus X squared, minus three square root of four minus X squared. So this is for one now moving on to two, which is just a standard integral. So to hear, integral off one over square root of four minus X squared. Ah, that&#x27;s a standard integral. So it&#x27;s gonna be signed in verse of X over square root of four, which is X over to So our final answer. So one plus to remember those were the region&#x27;s I labeled That&#x27;s gonna be minus three times square root off four minus X squared, plus sine inverse of X over two plus constant C. So this is our final integral here.

Robert Daugherty · Answer

Section seven out one problem 28. We&#x27;re dealing with an introduction to integration. Take needs. When I see this one, it&#x27;s probably best to break this into two separate intervals toe the integral of three X over square root of four minus X squared DX and then the other separate. Integral is just going to be plus one over the square root of four minus x squared DX So in the 1st 1 So when I look at this, if our to let you equal one minus x squared in de you is going to be minus two x t x so I can transform this integral. But the three out signed if I had a minus two x d acts, that is, if I multiply that integral by negative to would also need to divide by negative too, and then would have for minus X squared. And now you can see this is you. And then on the top you have, do you? So what This interval transforms into is minus three halves and then this is the integral one over square root of you. Do you? So this is minus three halves You to the 1/2 divided by 1/2. So this is just minus three. You to the 1/2. And remember our substitution for you. So this is just minus three square root one minus. Um, excuse me. Not a one. Sorry about this. This was four minus X squared, So four minus X squared. So that&#x27;s the first part. The second part, This is just Ah, you recognize this is ark sign. So this is going to be the art sign, X over two, plus a constant of integration. So my final answer will come from pulling these two pieces back together. Said this final answer is the arc sine of X over two, minus three square root four minus x squared, plus constant of integration.

Ramzi Deek · Answer

we have integral of two minus three X, divided by square root of one minus X squared. So let&#x27;s separate this into two fractions. So that&#x27;s to over square root of one minus X squared. Ah, minus three X over square root of one minus X squared. So for the 1st 1 will just put two out. So that&#x27;s one over square root of one minus X squared. The 2nd 1 That&#x27;s just that&#x27;s minus three square root of X over one minus X squared square rooted. So for the 1st 1 it&#x27;s a standard integral. So I&#x27;m gonna labeled a two sections here. So for one that&#x27;s too times so integral off D o D X over one minus X squared is same as sine inverse. So sign in verse of X over one who just just x So that&#x27;s the solution for one Now, for two gonna have negative three times integral of X over square root of one minus X squared. Well, in this case, I&#x27;m gonna do some substitution. I&#x27;ll just say you is one minus x squared. The U over D. X is minus two x So do you over minus two. X is DX So now we have minus three into and to go off X over square root of you times. Uh, do you over minus two x So x here and ex cancel. So I&#x27;ll take the negative to outside will get 3/2 times into grow off you to the minus half times, do you? So let&#x27;s solve from there. So that&#x27;s 3/2 times. So it&#x27;s I&#x27;d want to that powers times you to the half divided by half So that&#x27;s just multiplying by two. So that&#x27;s equal to three. You to the half. Well, we know that you is one minus X squared. So that becomes three into one minus X squared here. Square rooted. All right, so that&#x27;s for region to so one. Yeah, plus two. So our final answer would be so. One is to sign inverse of X. So that&#x27;s two signed in verse X plus three times square root one minus X squared plus constancy. So this is our final answer

Robert Daugherty · Answer

Section seven at 1 27 We have an integral here to Money&#x27;s three X over Route one minus X squared. We&#x27;re dealing with the introduction to integration techniques in this one. When I look at it, the one minus X squared square root that feels like an arc sine. But what do I do with the top of this Fraction? One of the key things to do here, let&#x27;s just break this into two separate inter grows. Okay, so let&#x27;s just change color for each one. So in the first interval, how can I handle to over the square root of one minus X squared DX and in the second, integral. How could a handle in a role of minus three acts divided by one minus X squared the axe? So let&#x27;s solve these separately and and put them all together at the very end. So this 1st 1 this was pretty straightforward. This is two times the integral of one over square root of one minus, explained the X that is the arc sine of acts. So this is to times iarc sign of eggs, plus a constant of integration. So that was done. Now look at the next integral here. Um, what if I were to let you equal one minus x squared, then d you would be minus two x dx. So what could I do with this? Integral To get a minus two x t x. So I could write this as the integral three times in a row. So if I put a minus two x de acts than ever, need to also divide by two in this case, and then you would see one minus x squared. So what this interval transforms to is sorry about that. When you look at this, you get three halves times the integral of one over the square root of you, do you? And so this is three halves times you to the 1/2 divided by 1/2 plus a constant of integration. So this just becomes three, um, you to the 1/2 So three you to the 1/2 plus a constant and remember you is one minus X squared. So this is just three one minus X squared, plus a constant. So putting all of those back together. So pulling these all back together to my final answer Final answer is just going to be to the Ark sign of X plus three square root of one minus X squared, plus constant of integration.

Foster Wisusik · Answer

Okay, This question wants us to find this integral. So since we have a square root, that&#x27;s usually where we should start by making you equal to the function underneath that So you is equal to X squared plus one. And this means that D U is equal to x d X four. Since you only have one copy of an ex do you over to is equal to x d x. So now for a little intermediate step, here&#x27;s what are integral look like So far it&#x27;ll look like X squared times x times square root of you D X or integral of X squared. Square it of you times do you over too four, 1/2 times the integral of X squared squared of you, do you? So now we need to figure out how to eliminate X squared. So if you see here you is X squared plus one. So that means X squared is just you minus one. So now we can plug in for that and get the integral of you minus one times squared of you. Do you divided by a factor of two and this is equal to 1/2 times the integral distributing out you to the three halves minus you to the 1/2 Do you or two times Sorry, 1/2 times anti derivative of three halves is 2/5 You to the five halves and then minus 2/3 you to the three halves plus C or distributing the 1/2 in and then plugging back. We get 1/5 time&#x27;s you, which is X squared post one to the five halves than minus 1/3 time&#x27;s X squared plus one to the three has plus C.

Problem

Evaluate the given definite integrals. $$\int_{\s…

Problem 32 Easy Difficulty

Evaluate the given definite integrals.
$$\int_{-3}^{-2}\left(3 x^{2}-2\right) \sqrt[3]{2 x^{3}-4 x+1} d x$$

Answer

$\approx 48$

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$\approx 48$

Basic Technical Mathematics with Calculus

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Precalculus Review - Intro

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

Grace H.

Heather Z.

Samuel H.

Michael J.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus