Practical Applications of Integration (1 Viewer)

[Aquawhite]

Okay. I have an upcoming assessment task and I need to determine the area from two photos of two different objects and then the volume of another. Working with the equations is fine as such once I have all the relevant data but this assessment task is very queer.

It is firstly in two parts and the first we need to say how we will work out the area/volume just by looking at the image (e.g. find the equation of the line of solid of revolution etc.) then on another day we do the calculations, but I have no idea how to find the equation of a line of a random object such as a container, just from an image....
The object might be a coke bottle... how am I meant to work with just a photo and then some of my own measurements? Can anyone help, if you understand this assessment task

 

[kaz1]

You can try simpsons rule, then square the result and multiply by pi. But I don't know if that will work.

 

[Timothy.Siu]

well for a coke bottle for example, if its lying flat then its basically just a parabola for the neck, and then a straight line, so u can work out the parabola if they give you a few points by solving a,b,c in y=ax^2+bx+c

 

[Aquawhite]

I'm quite sure that the teacher will have to give us some kind of ratios or lengths of lines to at least do something with it

Otherwise I'm stumped.

 

[Aquawhite]

You can try simpsons rule, then square the result and multiply by pi. But I don't know if that will work.

Interesting but still need an equation for the line.

 

[needFOOD]

Okay. I have an upcoming assessment task and I need to determine the area from two photos of two different objects and then the volume of another. Working with the equations is fine as such once I have all the relevant data but this assessment task is very queer.

It is firstly in two parts and the first we need to say how we will work out the area/volume just by looking at the image (e.g. find the equation of the line of solid of revolution etc.) then on another day we do the calculations, but I have no idea how to find the equation of a line of a random object such as a container, just from an image....
The object might be a coke bottle... how am I meant to work with just a photo and then some of my own measurements? Can anyone help, if you understand this assessment task

well you actually don't need the equation of the line of the coke bottle, simpson's rule (for example) works just on function values, so all you need is the distance between your function values (once you have the width of the bottle you can just make a nice number) then just slap in the initial height of the bottle as your y0, the final height as your yn, and any amount of other heights i hope i make sense, im not very good at explaining my ideas >.<

 

[Aquawhite]

To my knowledge and application of Simpson's Rule I have always used an equation in it still, thus the reason for finding the area under the curve, since every line has an equation. I'm gunna get some help and advice off a teacher tomorrow, if not... I'll do the best I can.

 

[kaz1]

To my knowledge and application of Simpson's Rule I have always used an equation in it still, thus the reason for finding the area under the curve, since every line has an equation. I'm gunna get some help and advice off a teacher tomorrow, if not... I'll do the best I can.

If you have the year 11 3unit cambridge book there's an example of using the simpson rule without a function in the Simpsons rule section in the integration chapter.

 

[Aquawhite]

If you have the year 11 3unit cambridge book there's an example of using the simpson rule without a function in the Simpsons rule section in the integration chapter.

Thanks. I will take a look in my Fitzpatrick Book that should have something. I currently am finising off the Couchman and Jones textbook and I found an example that does not use the function! ^_^ actually, the odd few.

I tested the idea with squaring the result and multiplying by pi and it worked in all my examples! Even the harder or weird ones.... thanks, this is going to get so much done extra for the assessment ... it's going to be super hard though. With the knowledge that this works, I'm going to use it for all the examples if I can't get an equation!

Of course I compared the answer to the proper method of integration with a formula of the line .. I am very pleased that squaring the result and multiplying by pi works...

Spread the word of the tiny discovery lol

Thank you all. I am grinning from ear to ear.