Calculus Problem

[volta]

I have a test tomorrow and my teacher handed out a review worksheet and I couldn't figure out this problem:

Find the volume of the solid generated by revolving the region bounded by y^2=4x and the line y=x about the line x=y.

I would really appreciate it if someone showed me how to work this.

 

[Chieftess]

That reminds me of the (1/x) trick question we had in Calculus class back in college... My Calculus skills are a little rusty though, and I don't have my trusty graphics calculator nearby (My sister has it -- or atleast had it).

 

[bhsup]

You could always try what I tried once. It didn't work for me, but your teacher may have a better sense of humor.

Just answer it, "Volta's Postulate".

 

[blackheart]

Just answer it, "Volta's Postulate".

 

[bhsup]

Eh, I was stumped on a question once and wrote "<my name> Postulate" as the answer. Yeah, I know, not really the meaning of a postulate, but hey I wasn't going to get it anyway and I was in a weird mood. My teacher wasn't amused.

 

[volta]

You could always try what I tried once. It didn't work for me, but your teacher may have a better sense of humor.

Just answer it, "Volta's Postulate".

I don't think that would work. My teacher is pregnant and usually isn't in a very good mood.

 

[Fifty]

Eh, I was stumped on a question once and wrote "<my name> Postulate" as the answer. Yeah, I know, not really the meaning of a postulate, but hey I wasn't going to get it anyway and I was in a weird mood. My teacher wasn't amused.

On the AP calc test I would just write out Euler's identity for any free-response problem I didn't get. I can't really remember it because I decided I dont' like math but I think it is like e^(i*pi)+1=0 apparently it is considered to be "beautiful" by math people but I'm not a math person so I dont get it.

 

[col]

Work out the two volumes for rotating y=x and y=root(4x). Usual integration method. Subtract.

 

[thetrooper]

...e^(i*pi)+1=0 apparently it is considered to be "beautiful" by math people but I'm not a math person so I dont get it.

e, i, pi, 1 and 0 are the most common 'symbols' in mathematics.

In this formula they are all combined.

Doesn't make me randy though.

 

[Mise]

I can't really remember it because I decided I dont' like math but I think it is like e^(i*pi)+1=0 apparently it is considered to be "beautiful" by math people but I'm not a math person so I dont get it.

Well it's normally stated as e^i.pi = -1. The Exponential function comes from things like population growth or radioactive decay. "i" comes from trying to find where a quadratic equation crosses the x-axis even when it doesn't actually cross the x-axis. Pi is the ratio between the circumference and the diameter of a circle. So you've got the growth rate of bacteria, a number that doesn't even exist, and a property of a circle you learn when you're 6. I don't think anyone could have guessed that if you put those three completely different maths things together, you'd get -1.

 

[Truronian]

&#960;&#8747;4x-x&#178;dx between 2 and 0, I believe

 

[volta]

:suicide: When I posted I typed it wrong. This is the real problem:

Find the volume of the solid generated by revolving the region bounded by y^2=4x and the line y=x about the line x=4.