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Question 22 ptsLet f (0,0) = #y + coa(a) + sin(Zy} Determine the line integral of f (#,y) with respect to arc length over the line segment from (1, 3) to (4,5)...

Question

Question 22 ptsLet f (0,0) = #y + coa(a) + sin(Zy} Determine the line integral of f (#,y) with respect to arc length over the line segment from (1, 3) to (4,5)

Question 2 2 pts Let f (0,0) = #y + coa(a) + sin(Zy} Determine the line integral of f (#,y) with respect to arc length over the line segment from (1, 3) to (4,5)



Answers

Evaluate $\int_{C} \mathbf{F} \cdot d \mathbf{r}.$
$\mathbf{F}(x, y)=\left\langle 2 y e^{2 x}+y^{3}, e^{2 x}+3 x y^{2}\right\rangle, C$ is the line segment from $(4,3)$ to $(1,-3)$

In the problem Be half those go indigo just inches five plus when inspire. Yes. So there lying segment and caution can be Get the mind ladies 15 people stew D and D and deep lives too Fine. Therefore we have side Esti people's to one more off dynasty people to go to. Yeah, if the s equals 05 If a sign off key more on our side as D did he Their whole equals two and it is indeed a fire. He is. God bless you. Spot duty densities dries up you over three 05 Their bodies toe upon three into one minute. Fire my entities 2 $50 Bantry So this is dancing.

So here a star by as This Star by Paramount tries those Cruyff and then combine together. Let's call this our part of the Circle Sea one on the sly segment C too, and has tried to Paramount Rice both of them. It goes from to zero, which is on the except that it's two zero two along the Y axis. So this is like the part of Circle First Quadrant. So you use a standard per mature ization access to co sign t wise to society. And he goes from zero two pi over, too. What is seat you Setu? We can use a standard per mature ization off the line and, uh, X should be forty wise to plus tea and sure, plus t and T goes from zero to one. We just do the integral arms separately and added Together, let's open another page So into grow they say that's to see one of our first. It goes from that This this is a parley with deal with C one first she goes from zero to pie over too Ex squares for coz I scurti the ex is negative to sigh Inti dt so that to sight see plus y square is for science security. The wise is it wise to co sign. So let's simplify this purse. Zero two pi over too, because there are eight that we have sign the sai skirt he co signed minus side d ho sai squared. So that's tried, Tio, solve this integral. See if there's any easy way or we just have to do it separately. Well, we showed them we can do a u substitution. I'm just feeling hours away. Wish my make this be easier. I guess we can just do it separately. There are no pie over to science square T co sign minus zero Tau pi over to side B coz I scurti for the press probably without you it was scientific. And for the second part, we let you horse Costa and this hot tea you'LL be negative sign titty And for this part to you co sign t So let's see aliens continue No eight I forget this It always should have eight times into grow zero two pi over too. Ah Sai squared! So we have awesome, sir. For the first part we do the substitution. So science chorus you square you square and, uh, cause and it is you and fun. Twenty goes from zero to pirate You signed. He goes from zero to what? And there's a second part coz I scored Tio issues Claire scientists next website It it is to you. And when he goes from zero to high over two coastline Chico's from one to zero. Yeah. So this is who can sew and that we should get a zero for this part on DH. Yeah, I'm not sure if it's actually easier way to do. It seems I do a lot of work to do to just to figure out this part and the seven price of pulling over into grow. So that's trying to do so. So the integration will just be on the second part on, uh, let's just do this for the seat you part xs forty What is two plus two and the Inter crows Franz From zero to one. Ex squares or sixteen t square The access to the sea Plus why squares too plussed he's square and the wide sea it is just It's just what? So it's just here. So zero to one, we have thirty two away with him is something at the city. Know what I'm doing here? This is not right. X is forty. So x square sixteen t score And the axis Just our forty. So this was sixty four T square, plus Andi Mitchell. Delighted. Delighted His one. So the wise teacher. Why square? Okay, so this square plus forty plus form. So we combined together sixty five square plus plus forty plus four. And so first time we got Cube over three, and we problem once. We got one of those street city five over three, plus your t square over too. So we find one you want to. So I want two times for us, too. And into grow four from zero to one. Keeps us for yes, for prostitutes. Six. Eighteen over three. So it's should be eighty three. And you can verify the answer yourself. His looks at her very lengthy computation, and I might make some arrow here. Hopefully the concept is clear

So line grow. Here we have two parts. First Part's thiss that we call this disco. See what this just called? This seat you and we do both interpreted added together. So that's try to Paramount tries both. Exit was to t y host Titi from there to one see to Mexico's too rusty Wife hosts one minus t. He also goes from zero to one. So that's two C one part first, uh, X plus two wise forty and tease from zero to one, it's prostitute wise forty The axis are to tt ex squares forty square do you wise dt? So we have zero to a one eighty plus forty square. So this was a times one over to because his teeth were over two. And we're pulling what? Plus for Similarly this won t few overthrew, probably while we have one or three. So we got four plus for over three. That's sixteen over three This twelve over three plus for over three in this off another page to do the sea to part of the crew exit host to Krusty. Why horse one minus two So too wise to minus two teams. So you have for my honesty. The Axis ditty X Square is a two plus Otis Corpus forty plus four and the wife is a negative one. TT so just changes toe minus a. Similarly, we, uh, simplify this. Minus t square minus forty, minus two minus five. T minus four class for there's a minus one over three is teachable red three. We probably want minus T score over two point one. The one over two. We got this. So six are two plus fifteen seventeen with a minus sign from So the original integral, original integral fish out. You know, this guy should be the the answer off these Hooper added together. So you're sixteen over three minus seventeen over a six. The first part is thirty two over three star. Sorry to over six social. Fifteen over six. Uh, and then we can divide by syriza five over two

Given a go to my ideas, this sea is presenting bicycle two x squared from zero Bama zero core Bless the lines. That bill from to come up or through $3 a musical will be something right going from here and then coming back here. So? So my ex one is a good day. Bye. One will be equal to the square. The Yes, Mandel Big will do the dairy with theirs off board into d d. Violent. So this is a girl to one square plus the woody who's squared. Really one. So this equals one plus 40 square D d one. My ex to will they will do to plus three minus two in duty is it will do to Les De then my by two is it will do full blurs. Zero minus Would into a deal was four minus four b there. Oh, my ideas to will be equal to X dash One more square plus minus Four walls were linking to. It was rude off 17 d d to therefore my cough. See the word? Yes, the big will do. Zero do four. Do we do the's Square? Underwood one minus. Woody's where the one plus 4 to 02 and do four minus were key crude 17 dd two. So this is a full toe to win toe one minus 40 square. Say is equal to you. I get the Esquire's ago to U minus one by 4 to 0 to four U minus one, but over into U to the power half into the U plus four Blue Zino, you're 17 outside. Four minus will be DD two. So this is a will do do 0 to 4 U to the power three by two Divided where were minor U to the power half divided by four. Do you less or does you know the road 17 Well minus school. Be deep, too. This is a wilder integration. This is you to depowered by going to before minus you to dip our tree by do before integration going from 0 to 4. Bless do Route 17 would be minus. You will d squared Or do you put the values we will get to been to 32 by four minus stayed by four plus two Road seven being minus 16 plus. So this is equal to seven plus 32 Road 17


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