integrate-each-function-by-using-the-table-in-appendix-d-a-good-representation-of-the-cables-betwe-2

Question

Integrate each function by using the table in Appendix $D$.
A good representation of the cables between towers of the $2280-\mathrm{m}$ section of the Golden Gate Bridge is $y=0.000370 x^{2}$ for $-1140 \leq x \leq 1140,$ where $x$ and $y$ are in meters. Find the length of the cables (see Exercise 35 of Section 26.6 ).

Vipender Yadav · Accepted Answer

So here on this problem, we need to find the length of this cable. And we are also given that this cable can be represented by an equation which is why is equals two 0.0 370 X. Square. And they were also given that X. Is greater than or equal to negative 1140 less than or equals to 1140 Now this is the input data. Now basically we have to calculate the length of the ark. So the length of the ark is of a cough from X. Is equal to a two X equals two. B. Is given by the formula as equals to integration A to B under route one plus. Do you buy over the X whole square dot dx. So this this basically can be treated as a cove and we can find the length of the scope by using this formula. Let me first find this dy over the X. So this is why we are giving us this much. So we can differentiate it. We can differentiate this. So do you buy over the X. Will be equals to two times 0.0 370 X. And it will be equal to 0.0 074 X. Now you can plug it here and if we have this negative 11 this one is A basically and this is B. So we can use this formula to evaluate this. So it will be cool too. This is equal integration. If we have a negative or 1140 to be is 1140 under roof. One plus dy over dx square. So this is this much zero point 00074 X. And it&#x27;s square. Since this is an even function. So we can use the integral of properties and it can also be written us two times 0 to 1140 Under route one plus 0.74 X. And its square dot dx. Now we&#x27;re going to evaluate this integral to find the length. So we&#x27;re going to use one formula which is the integration under route one plus X. Cold square. Not dx is equal to X over two. Under rule one plus a square square less one over to a natural log. This is a X plus. Underwrote one plus a square X. Square. So I&#x27;m going to use this formula to evaluate this integral. If you compare this formula with this integral, we can say that a we have 0.74 X. So you can plug it all this value here. So X by two as it is on the route or one plus ex a square expert. So it would be 0.74 X whole square. We can write this. We&#x27;re also plus one over to a natural look, if we have a 0.0 746 plus underwrote one plus a square X squared. So this is 0.74 X. And it&#x27;s squared. Now we have all the limits. So limit is 02 1140 And this too as it is. So it will be we can write it here. This is too as it is. Now, can you evaluate this into this expression by putting up in the limits upper limit minus the lower limit. And after putting the limits, we&#x27;ll get the final answer to be 2527 0.7 Which can be approximated to 2513 m. So this is the length of the cable. So I hope you have understood the problem. Thank you.

Ramzi Elkawa · Answer

All right, So for this question, were given a function. Why equals 0.0 037 times X squared to represent the hanging shape of a parabolic, um, bridge bridge line, Um, and were given that the whole length of the bridge is 280 across 1280 across. Um, and, uh, the height of it is 152. Uh, now, in order to ah, generate an approximation for this, The easiest thing for us to do is to again rely on a little bit of graphing software and our knowledge of lengthened girls. So we&#x27;ll take our derivative of R Y function. We&#x27;ll get why crime equals 0.74 uh, X. We can take that. Why, prime and plug it into a lengthen to grow. And the key thing is that we&#x27;re gonna know we&#x27;re going not from 0 to 12. 80 but from negative 6 40 uh, or to positive 6 40 So different side to the same Carrabba of the square root of one plus y prime s. So in this case, 0.74 times x That quantity squared DX And if we plugged that into some graphing software will quickly be able to figure out that our answer winds up being 1300 26 the 0.3 six meters approximately right.

Katelyn Chen · Answer

So for this country where a second find the life would change a cable. So first of all, we know that why is equal to 0.37 x squared. So that why prime agriculture 0.74 x and so they&#x27;re not our Our claims is equal to interval. It goes from native 6 42 6 40 I was of one plus 0.0. Does there something for X squared? The X which will get us and you go from number 6 46 40 I&#x27;m discourage one plus zero point Thank you for my sex for eight x squared the X which every use a calculator we show get approximately 1326 meters as our answer

Isaac Bruce · Answer

Okay. So yeah, I just then into brackets extra but sorry. Yeah, Why you go, Stan, into rockets each of the actual opportunity plus each other minus X watch trains Now on identity he sees that if you have e to the x plus, you did on minus six, all divided by truth. That&#x27;s function is equal to How about bullet co sign off X So with that in my if I do this radio, I deride the whole of this expression by two. And then I multiplied by true everything here Everything in the green bus this once have a biblical sign off extra battery, aunty. And then through time, staying just between throwing. Then we can write y to be equal trains the hyperbolic cool sign off extra trains. Okay, If we go forward, we can find out. Find that do vegetable spectral X Now that the river is evil there have a political scientist I have Obelix site which are sage and then using the chain we end up with the wide the actually see much times one about Tracy signs hyperbolic Sign off. Excellent Rienzi, You simplify it and you end up with a hyperbolic sign off. Excellent reasons now is that being said, we can find the accolades over the interval ministry In extremity we outdoor was integral from an incident between two squares off one flash sine squared X over 20. Yes. Now there&#x27;s another identity we see is that course Oh, hyperbolic co sign squared minus hyperbolic science way. Thanks. So you have course squared X minus Sign squared X To be a cultural one. He was a simple change of subject realized as one class Science Square X is the same as coarse square X So you can simplify and have squares off course Where that&#x27;s what meeting? Yes. Wow. Non losers Brief Instagram for my estranged are sh actual between us would an integral you end up with trains? His science. Excellent trinity. It&#x27;s basically a different thing you put in after 80 times since one minus science minus one and then you have foot seven parties do it

Ankit Gupta · Answer

first we start by drawing it off sketch so that we market coordinates on translate given information so that we can easily find the function. So we use the center as zero so that the letters 300 for the road and 1 50 on right 1 50 years left height is going as 1 20 to remind the coordinates minus one comma 1 20 on 1 50 coma 1 20 the center or the one x zero coma 20. Now we begin. Jack&#x27;s my height as age affects equals a giant X minus More alleged us hold square bless key. So from the translated information on it. Zero case 20 Xs let&#x27;s say the right coordinate. We take plug it in the 200.1 51 30 Which is why, well, like it into the equation on. So to find the value off, we simplify this further. I get the value of a has one upon to 25. Therefore, function is age X equals one born 25 x squared, less ready

Ankit Gupta · Answer

give it that the origin of the midpoint, such as the top in the double corners minus 6 40 Come on 1 52 and 6 40 comma Interested within this kids that the horizontal line, a 6 ft minus off minus six will be disabled underway there meters so helps. The height is on 52 m and the sketch will be The sketch will be this week. No, the finally standard decoration off the parable we can do X minus h hold quit because they couldn&#x27;t afford being toe by my escape. Here, Pitkamaki This zero comma and the point is 6 40 Come on, 1 50 do 6 40 minus Z equals 41 50 to minus zero. So that will give us music Will do oneto a double zero by 19. So in the equation which is exist where is equal to four into one toe 00 by 19 Divine minus zero that is Isaac Will 19 by 512 double zero. It&#x27;s squid, Another convict Creationist. We have to draw the table. Trouble off the grass will be in this way. If you have to see only a few points, we can get from zero who comes off 300. This would be the good off date. Creation on the table will be led. This that is a formula is working. Pointed 44 x 169.3 500 It is 92.77 and 600. It is 133 point from there.

Problem

Integrate each function by using the table in App…

Problem 45 Easy Difficulty

Answer

Related Courses

Basic Technical Mathematics with Calculus

Related Topics

Discussion

Top Calculus 1 / AB Educators

Heather Z.

Kayleah T.

Samuel H.

Joseph L.

Calculus 1 / AB Courses

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 28

Video Transcript

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Heather Z.

Kayleah T.

Samuel H.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

Basic Technical Mathematics with Calculus

Heather Z.

Kayleah T.

Samuel H.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Heather Z.

Kayleah T.

Samuel H.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus