Solids

In calculus, solids are formed by rotating a curve around an axis and integrating to find the volume. Typically the integration is of slices cut vertically to the axis of the rotation that formed the solid. Those slices are then integrated from one end of the solid to the other.

Example

Consider the region in the first quadrant that has an upper bound of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = \sqrt 2} and a lower bound of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = (\sec{x})(\tan{x})} , and on the left side by the y-axis. Find the volume of the solid formed by rotating the region about the line Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = \sqrt 2} .