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

• cmab
In summary, the conversation is discussing how to find the volume of the region bounded by the y axis, the line y=1, and the curve y=sinx using different methods such as disk and cylindrical shell methods. The individual is having trouble with integrating and is unsure if their answer is correct. There is also some confusion about the correct approach, with one person suggesting the disk method and another questioning if it will give an accurate answer. The conversation ends with a request for someone to verify the correct answer listed in a sheet.
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

cmab said:
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?

OlderDan said:
What method are you using, and what are you integrating?

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

disk method.

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

try cylindrical shell method

p53ud0 dr34m5 said:
try cylindrical shell method

In my paper it says use disk method.

cmab said:
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.

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 )

Last edited:

## 1. What is the formula for finding the volume of a solid bounded by a curve and two lines?

The formula for finding the volume of a solid bounded by a curve y=f(x) and two lines x=a and x=b is given by V = ∫abπ[f(x)]2 dx. This is known as the disk or washer method.

## 2. How do I set up the integral to find the volume of y=sinx bounded by the y axis and the line y=1?

First, we need to identify the limits of integration. Since the curve y=sinx is bounded by the y axis (x=0) and the line y=1 (x=π), the limits of integration are 0 and π. The integral will be V = ∫0ππ[sin(x)]2 dx.

## 3. Can I use any other method to find the volume of this solid?

Yes, you can also use the shell method to find the volume of this solid. The formula for the shell method is V = ∫ab2πx[f(x)-g(x)] dx, where f(x) is the upper curve and g(x) is the lower curve. In this case, f(x)=1 and g(x)=sin(x).

## 4. How do I solve the integral to find the volume?

To solve the integral V = ∫0ππ[sin(x)]2 dx, you can use integration by parts or trigonometric identities. The final answer should be V = (2π-4)/3 ≈ 0.81 units3.

## 5. Can I generalize this method to find the volume of any solid bounded by a curve and two lines?

Yes, the disk or washer method and the shell method can be used to find the volume of any solid bounded by a curve and two lines, as long as the curve is continuous and the lines do not intersect the curve. The limits of integration and the formula may vary depending on the specific shape of the solid.

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