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DarK1
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x = 2y - y^{2}
x = y
x = y
The disk method is a mathematical technique used to find the volume of a solid created by rotating a two-dimensional shape around a given axis, in this case the X-axis. The volume is calculated by summing the cross-sectional areas of the shape at different points along the axis.
The disk method is specifically used for finding the volume of solids of revolution, where a two-dimensional shape is rotated around an axis to create a three-dimensional object. Other methods, such as the shell method or washer method, are used for finding the volume of more complex shapes.
The formula for using the disk method to find volume when rotated about the X-axis is V = π ∫_{a}^{b} (f(x))^{2} dx, where a and b represent the limits of integration and f(x) is the function describing the shape being rotated.
No, the disk method can only be used for finding the volume of solids of revolution, where the shape being rotated is a simple curve (such as a circle or parabola) and the axis of rotation is perpendicular to the direction of integration.
The disk method has many practical applications in fields such as engineering, architecture, and physics. For example, it can be used to calculate the volume of a water tank, the amount of material needed for a cylindrical pipe, or the moment of inertia of a rotating object.