Need help with math
Last problem on the set of problems I Have to do and my mind is exploded and i've confused myself... Anyone know how to do this?
Find the area enclosed by an ellipse with the formula
(x^2/a^2) + (y^2/b^2) = 1 and where the upper half can be described with y = (b/a)sq.rt(a^2 - x^2) and the lower half with the same thing but with a negative... (-a, 0), (a,0) and (0,b) are points on the graph. That's all i'm given.
Graph is kinda like this:
http://i.imgur.com/Qpj0M.png
September 8, 2012
7 Comments • Newest first
[quote=charismatic]Essentially, anything elliptical (or circular) is better to express in terms of angles (parameterization, polar coordinates, etc.). They get rather messy in Cartesian form, as you're probably well aware of by now.
Since you're just starting integral calculus, I would go with the solution @ulti25 provided (multiplied by two, of course), but you should learn parameterization later on in this course.[/quote]
Polar coordinates makes finding the volume of round things a joke.
[quote=charismatic]Essentially, anything elliptical (or circular) is better to express in terms of angles (parameterization, polar coordinates, etc.). They get rather messy in Cartesian form, as you're probably well aware of by now.
Since you're just starting integral calculus, I would go with the solution @ulti25 provided (multiplied by two, of course), but you should learn parameterization later on in this course.[/quote]
Ah, great. I have to admit the way you did it does look much cleaner.
[quote=charismatic]@SunsetDews: a b pi is correct, please see my solution above.[/quote]
I looked at the solution, but unfortunately I'm not too familiar with the way you solved it...
When do you learn how to parameterize equations? I'm in the beginning of Calc II
[quote=ulti25]I'll upload a pic in a moment OP.
Don't want to worry you or anything but this is pretty easy stuff.
EDIT:
http://imgur.com/h4S7T.jpg
You need to multiply the result I got by 2 to get the area of the entire ellipse, didn't have space to write it below my result[/quote]
Wow, thank you I don't know why but the constants were messing me up. Book says the answer's abpi so I guess that's right
Thank you!
I'll upload a pic in a moment OP.
Don't want to worry you or anything but this is pretty easy stuff.
EDIT:
http://imgur.com/h4S7T.jpg
You need to multiply the result I got by 2 to get the area of the entire ellipse, didn't have space to write it below my result
(or you can look at charismatic's solution which is much more elegant, heh)
Can we get a general math help thread going? My Advanced Functions is giving me some trouble as well and I don't want to make duplicate threads
Nevermind. I thought it was a simpler question xD
You would definitely just want to use integration, assuming you know that.