evaluate-the-given-double-integrals-int_12-int_0x-y-x3-ex2-d-y-d-x

Question

Evaluate the given double integrals.
$$\int_{1}^{2} \int_{0}^{x} y x^{3} e^{x^{2}} d y d x$$

Tyler Moulton · Accepted Answer

we want to evaluate the devil and drill given. Ask the integral from 1 to 2. At the integral from zero to X Y X Q E to the X Y squared Dy Ds. This question is shown on the r standpoint or understanding of integration From the standpoint of Multivariate calculus. We&#x27;re going to solve in two steps. In each step we use single variable integration techniques where in step one we can do the inner integral here that zero X Y x q V x Y squared do I. And then in step two we evaluate the outer integral from 1 to 2 D X. Using our results from step one as our instagram. So proceeding us all we have are double integral is equal to the integral from zero to of half X squared E v xy squared zero X dx or the integral from zero to have X squared and x cubed minus half X squared dx. Thus we can evaluate our solution ask 1 60 x cubed minus 16 Excuse from 0 to 2 or other final solution. Each of the eight minus nine divided by six.

Patrick Vaughan · Answer

Hello. Today we&#x27;re given a double integral and were asked to evaluate it. So first, what we want to do is figure out what the first enrol is going to be with respect to were given the choice of why? Well, in our first inning role, which is, um, the integral closest Judy Variables question, uh, that one has an accident. So, um, if we&#x27;re evaluating acts and integrating an X for the upside on, that&#x27;s not gonna work. Um, So what we have to dio is undeclared that the first in a row will be our with respect to y And then the second in a row will be with respect to X because then when we plug in our evaluation of X, well, we&#x27;re already in our X variable. We&#x27;re integrating with respect acts in the second integration. So that&#x27;s why we do that. So I like to do is just sort of visually breaking down in part. And I meant declare that sion and then the outside of green. So our first integration is just gonna focus on the science part. So this is the integration from zero tax of to E to the X squared do you. Why? So what we want to do now is recognized that this funky expression right here is actually just a constant in terms of why? Because this is just an X variable, and we&#x27;re not gonna tackle at when we&#x27;re integrating perspective. Why? So the only variable in question is that d y? And while we know the integral of the Y, that&#x27;s just why So we have our constant retained to e to the X squared to eat the X to swear power. Um, and then times are why evaluated from your ex? Well, this gives us too e to the X squared We&#x27;re putting in for that. Why? So we get access or watch expression, and then we plug in for zero for the next one so that second term just cancels out and the ignore it. So we have to, um, e to the X squared Hi X. And we bring down our second in a girl. That green part. So from 01? Yeah. And now we tackle the second part of the integral. Well, this is where we might get a little confused. We&#x27;re going Well, how do we falter? This This is sort of a complex expression, and I&#x27;m not really sure how to do that. Well, that&#x27;s where we using old tools. And that tool is you substitution. So if we set you equals X squared and then the derivative of you equal to to act the X well, but he us that gives us all the parts we have our X squared. We have our two attacks. Yeah, so we can just plug it. So we have from 01 of e to the U you lots of pretty straightforward generation. So the integral of you is just did you and that&#x27;s it. So we can take our evaluation from 01 And then before we moved any further weaken, just say OK, well, and I just have to take my you plug it back in. So we get he the X squared, evaluated from 0 to 1. So we&#x27;ve done all of our immigrations, and now we just have to have been sure evaluation. So you have e to the one squared minus e 20 square. Well, either going squares either the one minus and anything to the zero power is one so erased. It is. Your power is one. So we have our final answer of E minus one, which is just a constant because, remember, he is just something like 2.7, and that&#x27;s how we do the double integration for the second problem.

Matt Just · Answer

Alright, here we have this double inter girl So euro to one two x four x of Okay, you do the X plus y Do I dicks, Okay. Anti derivative of e to the X plus y. It&#x27;s just itself. So that&#x27;s if we want to go ahead and evaluate Uh, so we just have each of the express y evaluate at four X So that&#x27;s going to be easy to the five x minus e to the three x The thanks. Mhm. All right. And then so we just evaluate where we take an anti derivative. So we get E to the five X over five minus e to the three X over three, evaluated from 0 to 1. Well, this is just eat of the 5/5 minus e cubed over three and then minus. We need to evaluate these zero. So that&#x27;s going to give me a plus one third and I&#x27;m minus 1/5. Well, one third, minus 1/5. So this is 15. A 5/15 minus three of her 15 to 215. So you do the five over five minus E to the 3/3 plus two over Team

Patrick Vaughan · Answer

blue today we&#x27;re given a double integration and were asked to evaluate it. So first off, we have to decide which and the role is with respect, which value Because we&#x27;re given integral with respect to y and one with respect to, um X. So the 1st 1 is going to be the inner role with respect to why. And the reason for this is because if we have, why equals, for instance, X squared. And we&#x27;re evaluating the expression after rejecting a girl than, um, the Y component turns into an X component, which makes it so that you can directly take the interval with respect to acts in the second integral. So that&#x27;s your internal hint in this problem for which order to dio three integrations and then as another important point when you&#x27;re taking the integral with respect, Why X is a constant. And I put this in red because it&#x27;s very important that you don&#x27;t, um, do something crazy, like do, uh, integration by parts there. Substitution. Not just because, um, I think that somehow access in Attica. Okay, now that we have that settled, we&#x27;re just gonna look at the first inter girl. Just gonna pull it out and ignore the other parts for now. So re reading this it immigration from X squared Teoh two x of Why de y The reason I did this is just to prevent mistakes from occurring on variables from being for God. So first, we&#x27;re gonna rate with respect. Why? So we have the immigration of why is why squared divided by two and then exit the constant So that&#x27;s retained. And then this is evaluated from X squared to two X and then as an aside, we always evaluate, uh, with respect to the top minus, um, evaluating with respect to the bottom. Ah, the orders port Important because you&#x27;ll get a different answer. I&#x27;m doing it one way versus the other. So plugging in for why we have our constant times two X square by two And that&#x27;s our left side and then minus Acosta. Next times x squared squared over to. So let&#x27;s, uh, simplify these expressions just to make it easier for him about next integration. So two x squared Well, that&#x27;s two square times X squared. So two squared is for and then x squares X squared. Uh, this is divided by two and then multiplied by X so before reduced to. And then the ex convict brought over into the expression and becomes X cubed. So this becomes to exe cute. And then similarly for the right expression. Don&#x27;t forget that. Fine. A fine circle it so we don&#x27;t so x squared, squared well, and exponents raise to another. Exponents is just the exponents from the lower one. Uh, what the, uh, exploded from me upper once that becomes X to the fourth power. So excellent force over to Well, these exes can be combined, and I becomes extra fit. So we have two x cubed minus X. If it our divided by two. And then now we can bring down our deac and our integration from 0 to 2. So let&#x27;s rewrite it. So our integration from 0 to 2, what we&#x27;re integrating is two x cubed minus next to the fest over to with respect to X. So everything checks out. It looks nice. Let&#x27;s do the integration. All right. So integration of X cubed is X and forth divided by four. We retain that que cops and then minus the integration second part. So the immigration is x 10 if it is X to the six divided by six and then we re seeing that 1/2 constant and then this is all evaluated from you&#x27;re in a to Well, let&#x27;s simplify before we evaluate So the two can be, uh, reduced. The floor so far becomes, too, that part becomes excessive force over to and then we have minus X 26 divided by, well, two times six. That&#x27;s 12 divided by 12. We can evaluate this from zero to to. So first we plug in the to. So we have to to the fourth power over to minus two. The six power over 12. Um, so that&#x27;s west side on minus are right side while we&#x27;re just playing in zero. So that whole expression just comes No. Zero. So, to to the fourth power. Well, that&#x27;s two times. Two times two attempts to such lengths to us for four times he was eight. He tends to is 16 so that&#x27;s 16 divided by two. Well, if we, uh, do this two more times to get the six power that is, um, 16 times to you, which is 32 and that 32 times two which 64. So that&#x27;s 64 all over 12. Well, weaken, simplify this. So 16 divided by two. Let&#x27;s be. And then 64/12. Um, that one. I actually through my calculator, and that is essentially five point storage repeating. These are always going to be nice numbers. All right, so eight minus five point through three. Repeating is two point 66 repeating that is the answer to this double integration, and that is everything we did to get there.

Tanishq Gupta · Answer

The question is to evaluate the Eid reckoning figure. They make a list immigration from minus 20 integrations from my best one extra square Leslye square. Yes, my movement towards a solution. First, we will be evaluating the inner integral. So taking the united together test immigration from my last one. Who? Excess where Less lice Where the x so a very, very waiting dating. Then it would be x you by three blessed EDS by square I, uh, limit from my next one not putting the limit. It will be a by three less do why square minus my next one by three My next buy spread So the I said for then everything people Good three less three white square. Now we will be evaluating. They are apparently dinner which is immigration from minus 20 brief less three by spread Do you buy? It will be free by less like you limit from minus 2 to 0 after putting the domestic big part zero my nest minus six minus T that is a close to minus minus 40 my nest 40. So beyond supporting it One question would be where to fucking thank you

Tanishq Gupta · Answer

The question is to evaluate the Eid reckoning figure. They make a list immigration from minus 20 integrations from my best one extra square Leslye square. Yes, my movement towards a solution. First, we will be evaluating the inner integral. So taking the united together test immigration from my last one. Who? Excess where Less lice Where the x so a very, very waiting dating. Then it would be x you by three blessed EDS by square I, uh, limit from my next one not putting the limit. It will be a by three less do why square minus my next one by three My next buy spread So the I said for then everything people Good three less three white square. Now we will be evaluating. They are apparently dinner which is immigration from minus 20 brief less three by spread Do you buy? It will be free by less like you limit from minus 2 to 0 after putting the domestic big part zero my nest minus six minus T that is a close to minus minus 40 my nest 40. So beyond supporting it One question would be where to fucking thank you

Problem

Evaluate the given double integrals. $$\int_{0}^{…

Problem 15 Easy Difficulty

Evaluate the given double integrals.
$$\int_{1}^{2} \int_{0}^{x} y x^{3} e^{x^{2}} d y d x$$

Answer

$\frac{e^{8}-7-e}{6}$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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$\frac{e^{8}-7-e}{6}$

Basic Technical Mathematics with Calculus

Lily A.

Catherine R.

Kristen K.

Michael J.

Vectors Intro

Vector Basics - Example 1

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

Lily A.

Catherine R.

Kristen K.

Michael J.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus