solve-the-given-problems-by-integration-a-force-is-given-as-a-function-of-the-distance-from-the-or-3

Question

Solve the given problems by integration.
A force is given as a function of the distance from the origin as $F=\frac{2+	an x}{\cos x} .$ Express the work done by this force as a function of $x$ if $W=0$ for $x=0$

Audrey Fong · Accepted Answer

were given the force function over here, F And we want to find the work done. Yeah. What is w if we are given the W zero and X close to zero. So we know that W is actually integrating your force we respect to X. Yeah. So they&#x27;ll be integrating two plus danger necks over cause I X. The X. Now I can split my term into two over crazy ex plus tension. Next over the course of the next Yes. Yeah. Now my first term is to Yeah one over Cosine will be sick connects. Plus now I have tangent X over one over cause I X. So I have danger necks one of the course I. X will be sicker next. So integrating my first term to see connects, I can bring my tool out before I integrate a second. When I integrate second I get long. Okay, what are see the next blast engine. X. Plus. Now integrating tangent X. C connects. I will get sick connects. Okay, so plus C when X equals zero, W equals zero. So Sabian, Yeah, sneakers one. We call signs tension zero will be just zero against second X. Second zero is one because I zero plus C. So I have to long one. Now this is zero plus one workers, centuries one plus C. So C is minus one. Therefore our final answer will be W is equals to two lawn mower or sea connects plus tension X plus. See the next plus see the SEs minus one.

Salamat Ali · Answer

here we fuss. Plot the four sources Displacement forces on y axis and displacement on X axis. Here we have. If Lord, this is zero. And here we have minus F. Lord, this is explored and this is two times off. Ex Lord, if you plot then this goes The line goes from picks mod and meet If Lord here given a one dimensional force therefore fix effects which is a function of X The world is simply equal to the area under the curve. So what will be called to integral off Ex Initial two x file force dx for about a The port is shown here we take explored to be a positive and the world done. He&#x27;s inactive. There&#x27;s the object moves from ex physical 202 x Is it going to explode? And the world is a positive as it moves from X physical Do it smart two x is equal to two x amount So this is negative here and here. It&#x27;s a positive since the 80 off a triangle we know any offer trying will be No, he&#x27;s the one or two times a based I&#x27;m altitude. Then the work done from X more acceptable to 02 X is equal to X. Marred is doubly. One is equal to minus X Lord times if no divided by two and the world done from X p Simple to fix Nod two X is equal to to explode is given by W to that easy Cool too well, um two ex lord minus X terms if f more divided by two. This gives us explored F Lord divided by two. The total work is then some off to So not who is one plus w two on this gives us minus one over to f more explored plus one or two explored f mort to be zero but be the integral for the work Done. Who can be written is a w integration from 0 to 2 Ex Lord, This is f into the function we have If more x divided by explored minus one d x are integrating this we get if more times x squared, divided by two ex Lord minus X integrating from zero to to explode this user stance her to be zero

Frank Lin · Answer

work done by the force pills. I want to compute this and ah, that is done by computing. If off our tea which access replaced by T minus I Inti why is replaced by one minus co sign t saw three minus co sign and the R pry off T is one minus co sign t ah, sci fi. So they&#x27;re thought products or the integral becomes in a goatee from zero to two pi and there&#x27;s that product So that product should be t minus tico sai inti minus sign t close Scientific society plus three society minus scientific society. So we just cross out this term So this one zero to two pi t minus he cause I he plus two side Did he this home So maybe we&#x27;ll have to do a little bit integration by part here. So in the growth Pecos I Inti, is you a sad issue this TV So you times you would just be sign He minus the to you is just one one dt so t sign t minus koh sai nt So here the entire derivative on the the entire derivative here should be t square over too, minus thiss minus T sai Inti plus Co sign T and the entire reviews Negative too Cose I t so this one cans are becomes minus sign minus koh sai nt probably to pylea four pi square over too We get to Pi square minus to pie Scientific I zero So we&#x27;ll have the worry about this time and ah co sign to pie This is the same as cousins who just want and the miners If you probably zero well zero here zero here cause I know this one so minus one so minus should be minus next before So here we have a problem to pi We got this minus republic Probably zero We&#x27;ve got an active one So here we got two Pi square minus one plus one so

Carson Merrill · Answer

So we have to use green serum in order. Thio, solve this So we already know I and R J components of the vector. So all we have to do now is take the or the first thing we have to do is take the partial derivative of those components. So first we&#x27;ll take the partial derivative of que with respect to X. So what that&#x27;s ultimately going to be is, um why squared citizens, That&#x27;s why squared and then the partial derivative of P with respect to why is just going to be X. So what we end up getting as a result of that is the double integral of white squared minus X. Yeah. Then, looking at the path followed by the particle, we see that the orientation as counterclockwise. So as a result, we can determine our bounds. Based on what they give us, we see that the bounds for X R 0 to 1 on the bounds for why are from 0 to 1 mine attacks. So because of that, we can make this do y the X, Then we&#x27;ll focus on this first inter role. Yeah, okay. On this first inter rule, we&#x27;ll end up giving us a one minus X cube over three, minus X plus X square and my fist. We take the integral again and we end up getting that. This is equal to a negative 1/12, as we see right there. So that tells us that the amount of work done was negative. 1/12. Andi, it depends on what the units are s so we can just say units.

Frank Lin · Answer

so find the work done. So we have the computer into growth. If the e r and the first step is to Paramount tries thiss so because that if wise teeth and access t square pross watts from one to two. So sorry T phones here to what? So then we can compute that have for far off t we repress exploit his square pross wad Replays Why buy t Expect hiss where process and our prime of tea which has taken a component wise so to tea and one so this integral will be the frontier will be taught product of these two So to TT square plus one square plus t e to the T square plus one So no next step It&#x27;s right out Antiterrorism it Eve. Well, it&#x27;s not that hard to see that both both parts are some kind of U substitution apartment. If you that t score plus one host you and to Teo ptu So this will be he square plus one cube over Siri plus e to the T Square plus one. Oh, yeah, too. So we have one over two years we&#x27;LL take the relative You knew the prostitute E in front. You get this and we plug it in one. We got to to kill witches. Eight eight over three plus one over to times Square. Miners were probably zero. Would you have won over three? No. And you&#x27;re probably zero. We get minus one over to eat with the one and we can collect. Term together. Seven over three, plus one over to his square, minus e.

Amit Srivastava · Answer

given a function. F picks Goma y is equal to to belie its with portion off CS Bicycle two X square from 0.2101 So let X physical duty you may get advising. Will do. He&#x27;s good. The X is equal to duty. You buys a quarto do de didn t My function X comma by Isaac Will do Percy through the X less ex divi. So I get 0 to 1 two into the exes Day T plus 0 to 1. What is X&#x27;d into devise toe t 80. So I get to be the only one. Plus, you wouldn&#x27;t do. You buy three little doing, so have a duty Bless duty you well 0 to 1 The list of the values two plus nobody to man&#x27;s It is came but

Problem 38 Easy Difficulty

Solve the given problems by integration.
A force is given as a function of the distance from the origin as $F=\frac{2+\tan x}{\cos x} .$ Express the work done by this force as a function of $x$ if $W=0$ for $x=0$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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Basic Technical Mathematics with Calculus

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

Catherine R.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus