Bazza's 3/4 Question Thread

[brightsky]

what panicmode said is basically how the 'formula' for rotating curves around the y-axis is derived.

[paulsterio]

Yes, but the inverse thing doesn't solve the problem, if you know the inverse, then essentially you can rotate it around the y-axis as well. For example,

y = x + 3 (for easiness sake)

for the inverse, x = y+ 3 so y = x - 3

so for the volume of rotation around the y - axis, we can do int((x-3)^2 dx) but that's essentially the same thing as int((y-3)^2 dy), you guys get what I'm trying to say right?

[b^3]

Yes, but the inverse thing doesn't solve the problem, if you know the inverse, then essentially you can rotate it around the y-axis as well. For example,

y = x + 3 (for easiness sake)

for the inverse, x = y+ 3 so y = x - 3

so for the volume of rotation around the y - axis, we can do int((x-3)^2 dx) but that's essentially the same thing as int((y-3)^2 dy), you guys get what I'm trying to say right?

Don't forget the in front of the integrals

[paulsterio]

I haven't done this in a while

[WhoTookMyUsername]

lol i just want to have all of my conceptual things in order before the SAC tomorrow, never know what Dr. G. might throw at you. or crush you with. or slowly and painfully destroy your soul with....

so does the inverse thing work then?

(yeah this is irrelevant for the exam, but just something like this could come up on sac)



paul, it's mainly for something along the general lines of

 y=f(x) is rotated around x axis between x = 1 and x = 2 (at these points y = 4 and y =

the volume is 2(pi) units cubed
calculate the volume if it was rotated around the y axis

?

[paulsterio]

I don't think you can work that out, think about it this way, I'll give you an example where it's different hang on

[paulsterio]

OK, say y = x^3 and y = 2x^2, they will both have the same value when x = 0 and x = 2

So with your question, y = f(x) is rotated around the x-axis between x = 0 and x = 2 (at these points, y = 0 and y = 8 ), the volume is...

What is the volume when rotated around the y-axis, it will be different depending on whether f(x) is x^3 or 2x^2 or whatever else, if you get what I mean.

[WhoTookMyUsername]

yep i get it it, so most likely there isn't a way XD

(but if there is an obscure conceptually difficult but possible way for a slightly modified quesiton i wouldn't be suprised if Dr. G. gives it to us xD)

thanks

[paulsterio]

Probably something to do with symmetry, that's obscure enough to be hard, uncommon enough that you wouldn't have seen it often elsewhere

[pi]

Is he still writing your SACs?


(if so, good! )

[brightsky]

have a go at this:

find the volume of the solid obtained when y = e^x between y = 1 and y = 4 is rotated around the y-axis.

[WhoTookMyUsername]

loge(y) = x
V
 = piS(4,1)[lny]^2 dy



for diff equations
dy^2/d^2 x

does that become (when flipped)
dx^2/d^2y?

[HenryP]

have a go at this:

find the volume of the solid obtained when y = e^x between y = 1 and y = 4 is rotated around the y-axis.

Well we know the formula to obtain the volume of the solid rotated about the y-axis is
So we know by rearranging the given equation.
So we have Integral from
Making the substitution , we have

Finally we have
Then Integration by parts to finish, although I don't think thats its in the course unless its changed from last year.
Hopefully there aren't any mistakes!

[pi]

dy^2/d^2x is not a fraction.


and for brightsky's question, I'd just cheat and use int by parts

[WhoTookMyUsername]

i know it's not a fraction. i mean for d/e where dy/dx = f(y)
(except second order)


and what's int by parts?