Need help with volume question (1 Viewer)

[BlueGas]

Is my answer right for this question? I'm getting the hang of finding the volume for questions like these, so I want to make sure if I'm doing it right. (Excuse the tilt of the picture)

 

[InteGrand]

Is my answer right for this question? I'm getting the hang of finding the volume for questions like these, so I want to make sure if I'm doing it right. (Excuse the tilt of the picture)

This is volume about the y-axis, so it should be

 

[BlueGas]

This is volume about the y-axis, so it should be

Oh wow, how didn't I realise that, thanks for that. But if it was about the x-axis, would my working out be correct?

 

[InteGrand]

Here, a = 0 and b = 4 (limits on the y-axis).

 

[InteGrand]

Oh wow, how didn't I realise that, thanks for that. But if it was about the x-axis, would my working out be correct?

Yes.

Edit: Hang on, you didn't write the expression correctly.

 

[InteGrand]

, not , since .

 

[BlueGas]

, not , since .

Okay, thanks for your help.

 

[InteGrand]

Is my answer right for this question? I'm getting the hang of finding the volume for questions like these, so I want to make sure if I'm doing it right. (Excuse the tilt of the picture)

Also, in your third line, how did the become ?

 

[BlueGas]

Also, in your third line, how did the become ?

Isn't it x^6/16? I took the 16 over, but I've been having trouble with taking numbers over to Pi, I don't seem to understand the way it works. Can you give me some examples of of volume questions and how it's done? Remember my last volume question I posted? I didn't know the way that works, I want to know how.

 

[InteGrand]

Isn't it x^6/16? I took the 16 over, but I've been having trouble with taking numbers over to Pi, I don't seem to understand the way it works.

Yeah it was an , but if you want to take the "16" out, note that it's actually a , so it stays a when you take it out.

 

[BlueGas]

Yeah it was an , but if you want to take the "16" out, note that it's actually a , so it stays a when you take it out.

So it's mean to be Pi/16, I need more revising on this.

 

[InteGrand]

So it's mean to be Pi/16

Yes, but this isn't specific to volume questions, it's true for integrals in general.

 

[BlueGas]

So I just fixed up my working out, it seems wrong from the final answer because it looks weird, but have I done anything wrong?

 

[InteGrand]

That looks right for rotation about the x-axis. The answer is probably giving the answer to the original question (rotation about the y-axis), which would explain why it doesn't agree with your answer.

Edit: Wait, the bounds are wrong for x-axis rotation.

 

[InteGrand]

You'll need to express in terms of for the rotation about y-axis, and then integrate with respect to y.