Intigration (volume of solids rotating about and axis)

In summary, the given solid is bounded by planes perpendicular to the x-axis at x=1 and x=-1. The cross-sections perpendicular to the x-axis are circles with diameters stretching from the curve y = -1/√(1+x²) to y = 1/√(1+x²), and vertical squares with base edges running from y = -1/√(1+x²) to y = 1/√(1+x²).
  • #1
jkw0002
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the solid lies between planes perpendicular to the x-axis at x=1 and x=-1 the cross-sections perpendicular to the x-axis are

A) circles whose diameters stretch from the curve y = -1/squrt(1+x^2) to the curve y = 1/squrt(1+x^2)

B)vertical squares whose base edges run from the curve y = -1/squrt(1+x^2) to the curve y = 1/squrt(1+x^2)
 
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  • #2
Welcome to PF!

jkw0002 said:
the solid lies between planes perpendicular to the x-axis at x=1 and x=-1 the cross-sections perpendicular to the x-axis are

A) circles whose diameters stretch from the curve y = -1/√(1+x²) to the curve y = 1√(1+x²)

B)vertical squares whose base edges run from the curve y = -1/√(1+x²) to the curve y = 1/√(1+x²)

Hi jkw0002! Welcome to PF! :smile:

Show us what you've tried, and where you're stuck, and then we'll know how to help. :smile:
 

FAQ: Intigration (volume of solids rotating about and axis)

What is integration in terms of volume of solids rotating about an axis?

Integration is a mathematical process used to calculate the volume of a three-dimensional solid that is created by rotating a two-dimensional shape around an axis. This process involves taking infinitesimally small slices of the solid and using them to determine the total volume.

How is the axis of rotation determined in integration?

The axis of rotation is typically given in the problem or can be identified as the line or axis around which the two-dimensional shape is being rotated to create the solid. It is important to correctly identify the axis of rotation in order to set up the correct integration formula.

What is the difference between using the disk method and the washer method in integration?

The disk method is used when rotating a solid around a horizontal axis, while the washer method is used when rotating a solid around a vertical axis. In the disk method, the radius of the disk is the distance from the axis of rotation to the edge of the shape, while in the washer method, the inner and outer radii of the washer are calculated based on the axis of rotation and the shape.

Can integration be used to find the volume of any solid?

Integration can be used to find the volume of any solid that can be created by rotating a two-dimensional shape around an axis. However, it is important to note that the shape must have a well-defined axis of rotation and the integration formula may vary depending on the shape.

Are there any limitations to using integration to find the volume of solids?

One limitation of using integration to find the volume of solids is that it can only be used for solids with well-defined axis of rotation. Additionally, integration may become more complex for irregular or non-symmetrical shapes, requiring the use of more advanced integration techniques.

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