Volumes by Disc Method

AP Calculus · Axiom Academy

Rotating curves around an axis to create 3D solids Step 1: Understanding the Disc Method When we rotate a curve around an axis, we create a 3D solid. The disc method slices this solid perpendicular to the axis of rotation into thin circular discs, then sums their volumes. Step 2: Setting Up the Integral To use the disc method, you need: The function f(x) being rotated The axis of rotation (usually x-axis or y-axis) The bounds of integration [a, b] Formula (rotation about y-axis): Step 3: Rotations About Other Axes If rotating around y = c (a horizontal line) or x = c (vertical line), adjust the radius: Example: Rotate about the x-axis from x = 0 to x = 2.

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