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Find the arc length of the curve r(t)Vsr , 2) Over the interval I[0. 21. Write the exact _ answer. Do not round:...

Question

Find the arc length of the curve r(t)Vsr , 2) Over the interval I[0. 21. Write the exact _ answer. Do not round:

Find the arc length of the curve r(t) Vsr , 2) Over the interval I[0. 21. Write the exact _ answer. Do not round:



Answers

Find the exact arc length of the curve over the interval. $$ y=\left(x^{6}+8\right) /\left(16 x^{2}\right) \text { from } x=2 \text { to } x=3 $$

Brooklyn number four, The lens is equal to take, ranging from 0 to 1 one plus boys where Weisberg plus two de Roy were injured. Age boy is equal to, uh, Why little or voice bread less. Um, and this can be simplified to and a secret to integration from 01 off, one over to spread review one plus U u plus to the you on this immigration for that is equal to invigoration from beautiful one. Oh, you plus 1/2 square of you, which is equal to integration from 01 Beautiful. But who's griddled off you plus aggression from your one on one over spurt of you you, which is equal to here u is equal to voice where? So you know why. Why so ah do boy is equal to 1/2. Uh, split you, Dean. So the integration for this for Melisse Ah, you or speak over to over 3/2. Plus, uh, you were her over, huh? From 0 to 1. Dr Those of institution. But why? Ah, but for you is equal twice. Where? So it's a big toe. Um, why? For 3/3 bus? Uh, why over her from 0 to 1. Do you think well after substitutions, apartment accidents were over

So we're trying to find the arc length of the curve R. Equals data squared. Um From fada equals 02 Theta equals chip. I so looking at this more closely we see that this is the formula for arc length and in this case we have G. Y. D. Theta. Equalling coast sign of theta. Okay I am Too theater uh minus data squared. Find data or crossing data in this case. Um This is my it's not right. There is actually going to be the X. D. Theta and then deride the theater is going to be science data times to theater minus fada squared co sign peter. So with that in mind we plug these values in and we have our integral that's from 0 to 2 pi of data times the square root of state uh squared plus four. You see that and we end up getting this answer as a result. Which can also be written as one third times four pi squared plus or the three halves My next eight. And as you see, that's the same exact answer.

Problem of about five He was over. Es. They were due to over three X or negative one off three j deeper to over three X forward. Ah, differentiation function. So any secret integration from one, 28 Ah, square one plus for over nine. It's for over three. Yes, you think with instigation from 1 to 8 of what? Gus who were three? Expert three. Where yet which is equal to upto simply education. Ah is equal to integration from 1 to 8. Ah, expert off nine X over. Over three plus four over a squared off nine. It's our approval. Three. Yes, it's a sequence investigation from 1 to 8. Uh oh. We're square off nine export over three plus four over. Export over three. Huh? Yet which is equal to 1/3. Immigration from 1 to 8. We're open nine x over three plus more over X power. Wonderful. Three. The x eso the integration for that is able to 1/27 nine x for over three loss More old over 3/2. Or what? From one wait upto service fusion. We can get that final answer is 1/20 seconds. 80 We're off then. My nuts. Europeans

It's clear. So when you read here so we have f of facts is equal to two X to the three house power. So that gives us a derivative. The three ex So 1/2 power one plus that they're a bit of square. Gives us one plus nine x someone we plug it in to our bowling formula. We're just gonna change acts to t you get the integral from one to x square of one plus 90 DT, we're gonna make you be equal to one plus 90. So nine e t is equal to do you so d t is equal to do you divide it by nine. This changes the limits of integration. So it goes from one to arks and it becomes ton. Since we're adding nine and one plus nine x you of 1/2 power, do you over nine. This is equal to one over nine turns 2/3 power 2/3 comes you to the 3/2 power. This is from 10 to one plus nine x. This gives us two times one plus nine x the three house power minus 20 square root of 10 over 27


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