Math Is Fun Forum

clumsy shark

Member

Registered: 2012-01-07

Posts: 13

Integration application

Find the volume generated by revolving the area bounded by Y^2 = X^3 , X=4
about the line X=1
Type y^2 = x^3 , x=4 on wolframalpha to check the area I mean
I can't understand how the area will revolve about a line lying within the area.
Many thanks in advance.:)

Last edited by clumsy shark (2012-05-29 20:37:47)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,646

Re: Integration application

hi clumsy shark

Does it mean like in my picture below?  The numbers are backwards because I had trouble getting the graph and had to flip it.

Boundary x = 4 is a mystery to me.  Could it be y = 4?

SEE POST #6

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Integration application

Hi Bob

Wouldn't it be infinite if you took y=4?

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,646

Re: Integration application

hi Stefy,

??  Not following where that came from.  I just wanted a boundary line.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Integration application

The boundaries are the curve y**2=x**3,x=4,x=0 and y=0.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,646

Re: Integration application

hi clumsy shark,

I've been out most of the day, but I didn't stop thinking about this.

Firstly I needed a decent graph so I used MIF's equation grapher at

http://www.mathsisfun.com/data/grapher-equation.html

Then I translated the graph one unit left and that version is shown below.

When x = 4 y = ± 8 so that gives you the limits and it's now being rotated around the y axis.

I would recommend you split the curve into two parts at y = 1 and integrate each separately.

Then it is just a standard volume of revolution.

Hope that helps.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Integration application

Now,that is a decent graph!

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,646

Re: Integration application

I'm rather pleased with it too.  But I owe it all to MIF's programming skills.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Integration application

Yes. We bow to you,oh,the mighty MIF!

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.