solve-the-given-problems-evaluate-the-following-integral-which-arises-in-the-study-of-hydrodynamic-3

Question

Solve the given problems.
Evaluate the following integral, which arises in the study of hydrodynamics: $\int_{H}^{h} \frac{A y^{-1 / 2} d y}{a \sqrt{2 g}}$

Dwijendra Rao · Accepted Answer

Hello Friends. We have to value the following integral which arises in the study of hydrodynamics. So we will take constant outside of the integral. So this this is he ain&#x27;t too cuz he upon capital a upon and to look to see in taking off to the power of man has won by two of leeway integral is from capital estrus manage upper limited the small it and lower limited edge so we can add it, yep. On Smalley square root of two G and take us. And all of this will be a Y to the power management by two plus months. This will even by two Upon one way to so a upon Smalley screwed up to G two square root of I capital edge. It&#x27;s more lead. So this will because to a upon route to G. Now we will put the limit that will be caused to you&#x27;re saying route small age minus scuttled off capital edge. So this will be close to score out of a upon a square out of G squirreled away a small edge money squirreled of capital edge. So this is the answer into route to of one and 2 Russi in the bracket is small edges cut out of a small village, small screwed up, couple it so this is the answer I hope you understood.

Amit Srivastava · Answer

let ah, heaven. Question is one and two Purvin by three That&#x27;s a cube. Work lie. It ive i que do you so let like you, Kal toh people. So you&#x27;re the physician will be three wise choir d y equal to duty. Hence Vice square D by will be Did he buy three? If we change, limit Reichel to one equal toe. And if I could, too Two powers one by three Shorty will be to power one by three Power three Surtees toe. Now I&#x27;m I will make little change in the question so limit will be oneto And why it can build an edge like you like you lie square and IV I you do you so final part will be went toe to like ust surface t square and vice card ey duty by three and e father like USA poverty The simplest way to solve this by part in simple one line see the shortcut method to solve this question using by knowledge terms it will be Hey, square e T minus 30 50 Bless do 50. And did you goingto so one bite See? It is full by the heat day. It&#x27;s glad minus food he powered cool and to keep our toe minus heritage E minus Dewey. Plus doing so. This will get also canceled. So final answer I will be won by three to e square minus.

Bahar Tehranipoor · Answer

in this problem, we want to find agent native to in the derivative agent to give to. So First, let&#x27;s find each of negative to say Asian native to equals in a roll of negative to plugging in negative two for X negative to do you over you scripless one we know right away this is zero because we&#x27;re integrating from one bound to the very same bound and graphically, you could think of it as you&#x27;re not covering any area because you don&#x27;t move. You&#x27;re going from native to *** to which isn&#x27;t not going anywhere, so there&#x27;s no area being covered. So the integral equal zero now, using the second part of the fundamental theme of calculus, what we&#x27;ll do is we&#x27;ll take the derivative. So let&#x27;s say the derivative of H of X equals it&#x27;s replacing you with X. So we get one over X squared plus one, and we can plug in negative to here. So we get the derivative of age. A native two equals one over native to squares, four for a sponge over five so these two values makeup or answer zero in one over five

Amy Jiang · Answer

Okay, so we&#x27;ll start rewriting, rewriting or radicals as exponents. Since it&#x27;s easier to work with, You know what it is that we have? Why? I feel terrible in half. Two times. So what? We Let&#x27;s you equal, right? You have 1/2. Well, then are derivative article 2 1/2 And then why did the power of inevitable? So that&#x27;s one over to Why&#x27;d you have 1/2? Why? I notice here, this question is exactly this portion here. So that&#x27;s equal to get you. So you have in a world of you over you e need to have you. And indeed you so that&#x27;s equal to eat You plus C and no replacing. Are you? You have Why are 1/2 pussy?

Carlos Pinilla · Answer

so me over this internal, the trail from Syria off to scrape it off through these You why, right from zero off? Do we? Why? More x e x on din between X square plus three. Why squared on ok minus X squared. Myers, Why squared that? He&#x27;s you see? So what is that into equal Dio we listen to go first into No, What we see is just see so busy volunteer routine those two loans on the in to be that room e excuse Why are well, they&#x27;re controls Syria? Yeah, why she recruits Gruebel and then what? We did a piece we&#x27;re gonna get, um so see will be just from that number eight in the 60 square minus y squared minus, uh D for not so minus X squared plus three y squared sort of. These will be well, usual. Expression is eight minus and minus of minus two X squared, minus and minus minus four more. Why, It&#x27;s word. So, uh oh, in green. Do it, Dad. With respect eggs, visit me equal. Jewell will eight x minus Dangerous off two X squared is minus 2/3 Knicks que This is a constant minus or um, Why you squared them? Six on that evaluated routine. You&#x27;re on 31 We have this last internal remaining. Why? From zero to square it off to. So when we do this devaluation there will get eight. Ah, nexus through our ate clams freak. Why, I&#x27;m going. Not mines. Who? Thirds who thirds. Ah, three. Why que my house more y squared times three. Why on the old that minus zero? Well, you&#x27;re zero. So we&#x27;ll be these terms on the time. You single too. So it them&#x27;s three. Why? So a rooms is three. Why my to nerves? Why, um three y cube, Mr Sex through Like you. Minus four times three. Or I see. That is why squared. That was wise. A like you limbs y cube. Simply find these. These So these this turns into most like you. Them. So thank you. From that councils before is there to have do them C squared comes y cube on. This is for times three. That&#x27;s why cube. So these with vehicle to why you, uh, them&#x27;s do times three squared minus, uh, or them three from the number is Siegel Doom. So these, uh So that was three. And then this is multiplying are free That he said to So because two time stood from three, that is the number. So this is equal to that? Um, three. My surgeries one. So that these expression, uh, and I would be is one waas robbers were obstructing toe. Both of those would be negative, so it would be plus, So the dog one will have a minor there. So mine is that one day some five. So it would be the soul expression with being Oh, this expression is gonna be people to eight times three. Our bodies are 24. Why? Around minus that&#x27;s of minus two times freedoms. Five. Ah, Why? Cube? So you have that in trouble? Yeah. That ain&#x27;t a gon respect. A white from zero discredit to these, uh, do what? On being trolled. That, uh, well, you will be superbly four. Why? Squared house minus are 235 times. Why do the fourth better before on that? Uh, awaiting you, Dean, it&#x27;s cooled off. Do zero will be. This is the well from the number is still skirt off to square. That is on, uh, do well, then these number would be minus. Do you see? It was five. Anybody, buddy four. I&#x27;m being screwed off Tool therefore musical toe two squared people before so that these four councils that we would have police only job will be staying for 24. That is 30 24 minus very. So it would be equal toe. His expression is so I mean minus six be seen drill since should be oh should be equal to Tu minus six my six.

Amy Jiang · Answer

Okay, so no zero that we have a square root of X inside our hyperbolic seek it and then we have one over the square root of so we can use Yusoff. Well, you&#x27;ve equal to the square root of X and then we have to you. That&#x27;s equal to 1/2 except of native 1/2. Yes, on well, with me, I that as one over it&#x27;s where of X Times two. Now let&#x27;s wanted part two on both sides. So we get to do you is equal to one over the square root of X the X this portion right here that&#x27;s to do you and then we have this portion inside here. But people to you know, let&#x27;s replace or endpoints or find are you and points. So at, um, X is equal to four. We have use equal to the square root of four and that&#x27;s it. Til on at X is equal to zero. R u is equal to tell. Okay, so we have the integral from 0 to 2 of sequence or sorry, Harper. Folic sequins squared of you to do you and we have another interval. Curtis, this is equal to, um it&#x27;s seeing hyperbolic seeking square is tangents Archibald tensions of you and then evaluated at two and girl to that too. Hyperbolic tensions of two minus to hyperbolic tangents. Zero. And this portion is equal to zero who got to hyper ball attendants to?

Problem

Solve the given problems. It is estimated that a …

Problem 47 Easy Difficulty

Solve the given problems.
Evaluate the following integral, which arises in the study of hydrodynamics: $\int_{H}^{h} \frac{A y^{-1 / 2} d y}{a \sqrt{2 g}}$

Answer

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Basic Technical Mathematics with Calculus

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

Anna Marie V.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus