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Volume Formulas
Formulas for finding volume of a shape using integrals
Question | Answer |
---|---|
Area: | A= ∫(from a to b) (R(x) – r(x)) dx |
Volume of a Disk | V= π∫(from a to b)(R(x) – r(x))^2 dx |
Volume of a Washer | V= π∫(from a to b)(R(x)^2 – r(x)^2) dx |
Volume around y=k | V= π∫(from a to b)(R(x-k)^2 – r(x-k)^2) dx |
Perpendicular Cross Sections: Squares | V= (from a to b) (R(x-k) – r(x-k))^2 dx |
Perpendicular Cross Sections: Rectangles with height=h | V= (from a to b) h (R(x-k) – r(x-k)) dx |
Perpendicular Cross Sections: Triangles with height=h | V= (from a to b) (h/2) (R(x-k) – r(x-k)) dx |
Perpendicular Cross Sections:Semi Circles | V= (π/8)∫ (from a to b) (R(x-k) – r(x-k))^2 dx |
Perpendicular Cross Sections: Equilateral Triangles | V= ((√3)/4)∫ (from a to b) (R(x-k) – r(x-k))^2 dx |