Volumes of revolution

Volumes of revolution

Volumes of revolution

Integration can be used to find the area of a region bounded by a curve whose equation you know.

Imagine that a curve, for example y = x², is rotated around the x-axis so that a solid is formed. The volume of the shape that is formed can be found using the formula:

Calculus

Differentiation

Differentiation

Calculus

Differentiation from first principals

Differentiation from first principals

Calculus

Differentiation of trigonometric functions

Differentiation of trigonometric functions

Calculus

Exponentials and logarithms

Exponentials and logarithms

Calculus

Implicit differentiation

Implicit differentiation

Calculus

Integration

Integration