# Calculating Volume of Rotated Curve: y=1/x, y=-1

• ziddy83
Thus, the volume is the integral of pi times the difference of the squares of the outer radius and inner radius with respect to x, evaluated from x = 1 to x = 3. In summary, the volume of the shape, with boundaries y = 1/x, y = 0, x = 1, x = 3, rotated about y = -1, can be found by calculating the integral of pi times the difference of the squares of the outer radius and inner radius with respect to x, evaluated from x = 1 to x = 3.
ziddy83
Hey everyone...I need to find the volume of the following shape...

$$y= \frac{1}{x}, y=0, x=1, x=3$$

rotated about $$y=-1$$

ok so, i drew out the shape, and for the radius i came up with:

$$r= \frac{1}{x} + 1$$

I think that's correct...so assuming that my radius is right, then the volume would be...

$$\pi \int_{1}^{3} ( \frac{1}{x} +1)^2 dx$$

did i set this up right? Thanks..

http://tutorial.math.lamar.edu/AllBrowsers/2413/VolumeWithRings.asp

Check out examples 3 and 4.

Last edited by a moderator:
ziddy83 said:
Hey everyone...I need to find the volume of the following shape...

$$y= \frac{1}{x}, y=0, x=1, x=3$$

rotated about $$y=-1$$

ok so, i drew out the shape, and for the radius i came up with:

$$r= \frac{1}{x} + 1$$

I think that's correct...so assuming that my radius is right, then the volume would be...

$$\pi \int_{1}^{3} ( \frac{1}{x} +1)^2 dx$$

did i set this up right? Thanks..

Your solid has a hole in the middle. The y = 0 boundary excludes a cylinder of radius 1 from the solid. You need the difference of the squares of the outer radius and inner radius.

## 1. How do you calculate the volume of a rotated curve?

To calculate the volume of a rotated curve, you can use the formula V = π * ∫(a,b) [f(x)]^2 dx, where f(x) is the function of the curve, and a and b are the limits of integration.

## 2. What is the formula for calculating the volume of a rotated curve?

The formula for calculating the volume of a rotated curve is V = π * ∫(a,b) [f(x)]^2 dx, where f(x) is the function of the curve, and a and b are the limits of integration.

## 3. How do you find the limits of integration when calculating the volume of a rotated curve?

The limits of integration can be found by identifying the points of intersection between the curve and the axis of rotation. These points will serve as the upper and lower limits of integration.

## 4. Can the volume of a rotated curve be negative?

No, the volume of a rotated curve cannot be negative as it represents a physical quantity and cannot have a negative value.

## 5. What is the axis of rotation in the formula for calculating the volume of a rotated curve?

The axis of rotation is the line around which the curve is rotated to form a solid shape. It can be the x-axis, y-axis, or any other line in the xy-plane.

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