evaluate-the-given-definite-integrals-int_14-x3-2-d-x-2

Question

Evaluate the given definite integrals.
$$\int_{1}^{4} x^{3 / 2} d x$$

Dwijendra Rao · Accepted Answer

Hello France. We have to evaluate the given definite integral that is integration of to the power three. I do dx LTD is 1 to 4. Low limit is one and a limit is four. So the integration of actually Power three where they will be extra the power three were to president upon 32 plus one. And the lower limit is fun and the parliament is for So this will be a cost to actually power if I were to upon Forever 2 12. So this will be a costume To have 1 5 4 to the power of five x 2 -1 to the power off five or two. So this will be consumed 2154 to the power five x 2 will be to the power of five that is 32 minutes we want. Okay So there is two and 2:31 upon five. So it will be cost to 62 upon five. So this is the answered. I hope you understood. Thank you.

Doruk Isik · Answer

in this problem. Where us to? People like to give in Tegel. Uh, we know that the entire director for dysfunction iss ex cute, minus exit afford divided by four. The older they have more. Board right here. We need Thio. Relate this at 44 4 s. So this will be like that point for 6 to 4 by 16 minus. Now you&#x27;ll like that point once or the lower point? Well, I won minus born over 16 and promise we find the answer to be seven 53 derived by 16.

Ian Maurer · Answer

into girl on this one from 1 to 4. Uh, three X square, my ass X cubed over 40. Yes. All right. You can do each piece separately. Anti derivative of three X squared would be three extra. The fair&#x27;s over three. So it&#x27;s gonna cancel those trees. Anti derivative of X cubed would be extra the fourth. And then this is four times for there was already a four on the bottom and we need to divide by another four. So I&#x27;m gonna just treat that as a 16. We moved on to the next line. We&#x27;re closing in four and are living in one. So we have four cube minus for to the fourth, over 16. That&#x27;s my effort, Cap Capital F would be. And then after Bay one to the fared minus one to the fourth over 16. All right, So Ford of the third is 64 for to the fourth over 16 is actually just 16 because, uh, it&#x27;s like canceling out two of the force. This is four squared, So I&#x27;d really set to calculate for spring. I&#x27;m over here. We have 12 The third, minus one to the fourth is just 1/16. Bring that up here just to finish it out. 64 minus 16 is 48. We have 48 minus one double negative. 1/16 So I get 47 1/16.

Foster Wisusik · Answer

Okay, This question wants us to find the following anti drink. So to do this, we see we&#x27;re dividing but a function inside of the Cube. So let&#x27;s pick that to be, are you? So let&#x27;s have you be equal to X squared minus four. Because if we do this, we see that D U is equal to two x d. X, but we only have one axe in are integral. So let&#x27;s divide both sides by two. To get d&#x27;you over to is equal to x d. X. So now we can substitute and for everything. So we have the integral of won over you cute times, d&#x27;you over too or 1/2 times the integral of you to the negative three d U. And if we do this anti derivative, we get 1/2 times you to the negative two divided by negative, too. Let&#x27;s see or negative 1/4 you to the negative two plus C and plugging in. We get negative 1/4 times you squared, which is X squared minus four, and we&#x27;re squaring that plus C and that&#x27;s our answer

Linh Vu · Answer

in it. You knew discussion in the fastest way when ionized that tree function inside a break it Here we have this one this and is but the first Onda 30 is odd function. Therefore were considered the ICO limit. Never mons want you want They are different. Either sign on for the or function if we do the same limit from left to right And the Indigo e coaches. Aargh! You know, it&#x27;s that we have an integral over months. Ain&#x27;t your eye on the old function And then the bank Listen, almost languages are there for what you need to do inside here but inside. And we do it for months and you remember even function Well, you go, Joe from I promise that you&#x27;re I only they were wondering about you on the even function here. So that&#x27;s off the home front into go interrupt you from two times from 0 to 1 now, uh, minus two X squared the angst and ego Jill Manus for expert TV. Every tree in the event it comes out. You won, *** wrinkled your man. It&#x27;s far from the tree

Yiming Zhang · Answer

here have the ones who once Q minus two x squared plus four X d eggs so badly Merete the integral equals to some of into of each term. I mean, no, these that&#x27;s these two terms are our function into winning over a symmetric interval. So the goes to zero. The only thing left is that in two times, if you want one square the X which is equals to make two tons 0 to 1 x squared DX, then times too. But the symmetry so is like four times 0 to 1. The institute s cute over three from 0 to 1. So the final answer before over three neck too.

Problem

Evaluate the given definite integrals. $$\int_{4}…

Problem 5 Easy Difficulty

Evaluate the given definite integrals.
$$\int_{1}^{4} x^{3 / 2} d x$$

Answer

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