Volumes (1 Viewer)

[Vampire]

I've got a test coming up (3 unit) and it has "volumes" in it. I'm guessing this is harder 2 unit volumes but i'm not sure...and exactly what is harder 2 unit volumes??

Any help is appreciated...

 

[jm1234567890]

I remember 3unit volumes were just volumes of revolution, but rather than using the standard formula. integral of pi * y^2 dx or whatever.

You had to derrive the formula since the revolution axis could be different.

 

[acmilan]

We did y^2dx integrations in 2 unit also.

Most likely it will be volumes involve functions that you dont learn how to integrate in 2 unit. Such as inverse trig functions or stuff like sin²x

 

[Trev]

We did y^2dx integrations in 2 unit also.

Most likely it will be volumes involve functions that you dont learn how to integrate in 2 unit. Such as inverse trig functions or stuff like sin²x

We did not encounter integrating inverse trig in 3 unit 'integration'. I think it is only covered in 'inverse trig' and 4 unit integration topics.

 

[acmilan]

What i meant was integrating functions that result from differentiating inverse trig functions. To add on that, you can integrate inverse trig functions on their own using 3 unit methods, so i dont see why they wouldnt ask to find the volume of an inverse trig graph

 

[Pace_T]

Substitution method for determining volumes, maybe?

 

[rama_v]

It could simply be 2 unit questions except that you need to add two volumes or take away intersecting volumes etc. For example see the last question in this JR paper to get an idea.

 

[jm1234567890]

It could simply be 2 unit questions except that you need to add two volumes or take away intersecting volumes etc. For example see the last question in this JR paper to get an idea.

that's right, I remember now.

integrating on different axis was for 4unit.

 

[acmilan]

that's right, I remember now.

integrating on different axis was for 4unit.

er are you sure? I remember doing that in year 12 and I didnt do 4 unit. Possibly im thinking of something different to you

 

[jm1234567890]

er are you sure? I remember doing that in year 12 and I didnt do 4 unit. Possibly im thinking of something different to you

mabye... i don't know any more tooooo long ago

 

[acmilan]

It may have just been some random thing i did on my own if its not in the 2 or 3 unit course

 

[Vampire]

Which books Steele?

 

[acmilan]

Fitzpatrick had one of those from memory

 

[acmilan]

Something like this perhaps:

Fitzpatrick exercises 26(d)

44. Find the volume of the solid of revolution formed by rotating the curve y = sinx between x = 0 and x = pi/2 about the x-axis. Hence, find the volume of the solid formed by rotating the curve y = sin^-1x between y = 0 and y = pi/2 about the y-axis.

 

[Trev]

Slide, you have way too much time on your hands.
But yeah, any competent 3 unit student should be able to integrate y = sin^-1x by knowing x = siny.