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In mathematics, in particular integral calculus, disk integration (the "disk method") is a means of calculating the volume of a solid of revolution. This makes use of the so-called " representative disk". The idea is that a " representative rectangle" (used in the most basic forms of integration -- such as ∫ x dx) can be rotated about the axis of revolution; thus generating such a disk.

As volume is the antiderivative of area, the integral can be used to find the volume, V, of an integrated " family" of disks. The necessary equation, for calculating such a volume, is slightly different depending on which axis is serving as the axis of revolution. These equations note that the area of a disk (one which has no height, and no volume) equals: pi (π) multiplied by the disk's squareA square as a geometric shape is described and illustrated at square (geometry). There are other concepts derived from it: the geometric unit square; the square units of measurement, such as the square mile, square meter, square kilometer, square inch, and radiusThe word radius ( Latin for "wheel spoke"; plural radii pronounced ray dee-eye has several meanings in English: In classical geometry, a radius of a circle or sphere is any line segment with one endpoint on the circle (i. the circular boundary) and the ot (r²). The volume of a representative disk equals: πr²which is in turn multiplied by the disk's length (dx) or height (dy), that being some numberA number is an abstract entity used to describe quantity. There are different types of numbers. The most familiar numbers are the whole numbers {0, 1, 2,. denoted by W and the natural numbers {1, 2, 3,. used for counting and denoted by N . If the negative approachingIn mathematics, the concept of a limit is used to describe the behavior of a function, as its argument gets "close" to either some point, or infinity; or the behavior of a sequence's elements, as their index approaches infinity. Limits are used in calculu zero.

• Horizontal Axis of Revolution
  • V = π ∫ [R(x)]² dx
• Vertical Axis of Revolution
  • V = π ∫ [R(y)]² dy

For instance, consider the functionIn mathematics, a function is a relation such that each element of a set (the domain is associated with a unique element of another (possibly the same) set (the codomain not to be confused with the range . The concept of a function is fundamental to virtu f(x) = √( sin x), as it exists between x = 0 and x = π. If one imagines this function being rotated around the x- axisAxis has several uses: In mathematics, an axis is a straight line around which a geometric figure can be rotated. An axis of symmetry is a line with respect to which a body can be symmetrical. The term is also applied for the axis of a graph; the horizont (so as to create a solid of revolution); then, the radius of that solid (for any value, x) is equal to √(sin x). Using the above formula, one can determine the solid to have a volume of: π ∫ [√(sin x)]² dx -- when evaluated from 0 to π. The solid has a volume of 2π.