The
**disk method** refers to the technique used to find the volume
formed by a shape that revolves around an axis, AND the axis
itself forms one of the boundaries of the plane that is
revolving.

For example, if a simple line revolves around the 'x' axis over a range of x values, the volume can be visualized as series of disks formed as each point along the line revolves around the 'x' axis. As the point revolves around the axis, it forms a circle whose area is Πr2 . The radius of this circle is the value 'y' of the
function evaluated at a given 'x' (or the value of 'x' evaluated
at a given 'y').

The volume of the shape is found as we integrate over the circle's area as each value of 'x' or 'y' changes.

If the region bounded by the function (a plane) rotates around the 'x' axis over an interval of 'a' to 'b', the volume is expressed as:

$$\mathrm{V}={\int}_{\mathrm{a}}^{\mathrm{b}}\Pi {\left[f\left(x\right)\right]}^{2}dx$$

If the function revolves around the 'y' axis, the volume integrates over the range of 'y' values within the interval:

$$\mathrm{V}={\int}_{\mathrm{a}}^{\mathrm{b}}\Pi {\left[f\left(y\right)\right]}^{2}dy$$

In this case, we look for the volume of a solid whose shape is formed by a function y = x2 over the interval [-2,2].

For example, if a simple line revolves around the 'x' axis over a range of x values, the volume can be visualized as series of disks formed as each point along the line revolves around the 'x' axis. As the point revolves around the axis, it forms a circle whose area is Πr

The volume of the shape is found as we integrate over the circle's area as each value of 'x' or 'y' changes.

If the region bounded by the function (a plane) rotates around the 'x' axis over an interval of 'a' to 'b', the volume is expressed as:

$$\mathrm{V}={\int}_{\mathrm{a}}^{\mathrm{b}}\Pi {\left[f\left(x\right)\right]}^{2}dx$$

If the function revolves around the 'y' axis, the volume integrates over the range of 'y' values within the interval:

$$\mathrm{V}={\int}_{\mathrm{a}}^{\mathrm{b}}\Pi {\left[f\left(y\right)\right]}^{2}dy$$

In this case, we look for the volume of a solid whose shape is formed by a function y = x

Revolving solid planes - disk method

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