Can U Use Simpsons Rule To Work Out Volume!!!!!!!!!! (1 Viewer)

[p00_p00]

Well can u????

 

[fatmuscle]

um... depends on the question???

 

[Lazarus]

Yes, you can - it will only be an approximation, though.

If it's being rotated around the x-axis:

V = Pi * Integral(y^2 dx)

You can use Simpson's rule to approximate the value of the integral in that equation.

Draw up a table for sub-interval values as you normally would, then simply square each of those values before you substitute them in for the integral.

 

[-=«MÄLÅÇhïtÊ»=-]

Yup

u do it the same way as u would do for working out area.

Note: You don't work out area, square it and times it by Pi


u apply the rule to (y^2), and then u times by Pi.

 

[Lazarus]

I didn't say that you square the area, I said that you "square each of those values [in the table]", which will give you the same sub-interval values as if you had used f(x) = y^2.

 

[-=«MÄLÅÇhïtÊ»=-]

i didnt say u were wrong dood

i juz added my explanation coz ur one was abit ambiguous on how to actually do it.

But now that ive had another look at ur post...
"simply square each of those values before you substitute them in for the integral."

Dat's kinda confusing..
Don't you change the abcissor depending on the equation? Squaring is only a limited case if u have a simple curve like y=x^2.
If u have y=sin^2(x), u dont square it..
u sub the x into y=sin^4(x)...
If u square it and put it back into equation u get
y=sin^2(x^2)

hard to explain
im prolly interpreting ur post wrong.

 

[Lazarus]

Perhaps it was ambiguous.

I meant that you could simply square the y values in the table before substituting them into Simpson's rule.

 

[-=«MÄLÅÇhïtÊ»=-]

dats wrong aint it?
that will only work if u have y=x^2n kinda curve

read the last bit of my previous post

 

[-=«MÄLÅÇhïtÊ»=-]

Maybe i should make the syntax clearer

"If u have y=sin^2(x), u dont square it..
u sub the x into y=sin^4(x)...
If u square it and put it back into equation u get
y=sin^2(x^2)"


this is more correctly typed:

If u have y=(sinx)^2, u dont square it..
u sub the x into y=(sinx)^4...
If u square it and put it back into equation u get
y=[sin(x^2)]^2

 

[Lazarus]

No, it's not wrong.

Using your example:
y = sin^2(x)

Let's say one of the x-values is pi/3.

Method #1:
y^2 = sin^4(x)
y^2 = sin^4(pi/3)
y^2 = (sqrt(3)/2)^4
y^2 = 9/16

Method #2:
y = sin^2(x)
y = sin^2(pi/3)
y = (sqrt(3)/2)^2
y = 3/4

Squaring this y-value:
y^2 = 9/16

You're not squaring the x-values, remember.

 

[-=«MÄLÅÇhïtÊ»=-]

oh ic where i misinterpreted u

u initially said
"simply square each of those values before you substitute them in for the integral"

I thought u meant square the x values

coz u dont sub y values into "integral"
the only values u sub into integral are x values (of course we're talking about integrating wrt x)


But ok, ur later post was correct.

 

[Lazarus]

Simpson's rule is, for all intents and purposes, equivalent to the integral, and is what I had in my mind when I wrote it.

 

[-=«MÄLÅÇhïtÊ»=-]

not really...
u sub in limits (x) into integral, and u sub in [f(x)] into simpson's rule..

 

[Lazarus]

We really have trouble communicating, don't we?

The end result of Simpson's rule is, for all intents and purposes, equivalent to the end result of the integral.

 

[-=«MÄLÅÇhïtÊ»=-]

dats like saying burgers and fries are the same thing coz they both feed ur stomach. And when i say 50 pieces, im not talking about number of chips, im talking about number of burgers


anywayz, i need to hit the books

 

[Mordenkainen]

is it the same for trapezoidal rule? (i.e. same steps)

 

[Lazarus]

Yes.