Find the volume y=sinx, bounded by the y axis, and the line y=1

[cmab]

Can anybody help me find the volume y=sinx, bounded by the y axis, and the line y=1. The axis of revolution is the line y=1.

I tried so many times and I can't find the correct answer, in the sheet it says (pie^2)/2 - 2pie

 

[OlderDan]

Can anybody help me find the volume y=sinx, bounded by the y axis, and the line y=1. The axis of revolution is the line y=1.

I tried so many times and I can't find the correct answer, in the sheet it says (pie^2)/2 - 2pie

What method are you using, and what are you integrating?

 

[cmab]

What method are you using, and what are you integrating?

[int a=0 b=1] pie(arcsiny)^2 dy

disk method.

 

[cmab]

I don't know if I did good, cause I'm uncapable of integrating it.

 

[p53ud0 dr34m5]

try cylindrical shell method

 

[cmab]

try cylindrical shell method

In my paper it says use disk method.

 

[OlderDan]

Can anybody help me find the volume y=sinx, bounded by the y axis, and the line y=1. The axis of revolution is the line y=1.


[int a=0 b=1] pie(arcsiny)^2 dy

disk method.

I don't think you are looking at it right. As I see it, the radius of a disk centered on the axis of rotation is 1 - sin x and the thickness of the disk is dx. The integral runs from the y-axis (x = 0) to the value of x at the intersection of y = 1 with y = sin x.

 

[jtox]

I was thinking the same thing, and maybe it's just me, but if you finish integrating that, won't you get an answer that's off somewhat? (I think by about +$$\textstyle{\frac{\pi^2}{4}}$$, otherwise I'm totally and utterly wrong )
cmab, can you doublecheck that answer that your book states?