Thread: Volume of revolution

1. Volume of revolution

The area between the curve y=sin2x, the x-axis between 0 and 1 and the line x=1 is rotated through 360 degrees about the x-axis.

a) Sketch the area described.
b) Write down an integral expression for the volume of the solid formed.
c) Find this volume.

That's the whole question, I provided a,b, and c for completeness. What I need some explanation on is with regards to the line x=1.
I drew 2 functions on the same set of axes: y=sin (x+pi/4) and x=1...
Is that right?

2. Originally Posted by bhuang
The area between the curve y=sin2x, the x-axis between 0 and 1 and the line x=1 is rotated through 360 degrees about the x-axis.

a) Sketch the area described.
b) Write down an integral expression for the volume of the solid formed.
c) Find this volume.

That's the whole question, I provided a,b, and c for completeness. What I need some explanation on is with regards to the line x=1.
I drew 2 functions on the same set of axes: y=sin (x+pi/4) and x=1...
Is that right?
Um.. no. I think the x = 1 is just there to enclose the area.

The question is worded crappy. It should be:

Consider the area in the first quadrant bounded by y = sin (2x) and x = 1.

Less confusion..

$V = -\frac{1}{4}\pi cos(2)sin(2) + \frac{\pi}{2} \approx 1.86799$

3. Well, then there is still two equations: y=something and x=something, so how am I supposed to work that out?

The answer in the book only works out the solution with the y=sin2x equation, which I am able to work out
However, I don't understand the x=1. If it still bounds the area, then isn't it still one of the equations....?

4. Originally Posted by bhuang
Well, then there is still two equations: y=something and x=something, so how am I supposed to work that out?

The answer in the book only works out the solution with the y=sin2x equation, which I am able to work out
However, I don't understand the x=1. If it still bounds the area, then isn't it still one of the equations....?

No it's not. It's just put there so that you know that your limits of integration will be from 0 to 1 but you only use the y = sin(2x).