# A report on Integral, Geometry, Mathematics and Calculus

In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data.

- IntegralGeometry is, with arithmetic, one of the oldest branches of mathematics.

- GeometryMathematics is an area of knowledge that includes such topics as numbers (arithmetic, number theory), formulas and related structures (algebra), shapes and the spaces in which they are contained (geometry), and quantities and their changes (calculus and analysis).

- MathematicsCalculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations.

- CalculusIt has two major branches, differential calculus and integral calculus; differential calculus concerns instantaneous rates of change, and the slopes of curves, while integral calculus concerns accumulation of quantities, and areas under or between curves.

- CalculusAlong with differentiation, integration is a fundamental, essential operation of calculus, and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others.

- IntegralCalculus, consisting of the two subfields infinitesimal calculus and integral calculus, is the study of continuous functions, which model the typically nonlinear relationships between varying quantities (variables).

- MathematicsThis was a necessary precursor to the development of calculus and a precise quantitative science of physics.

- GeometryIn calculus, area and volume can be defined in terms of integrals, such as the Riemann integral or the Lebesgue integral.

- GeometryArea can sometimes be found via geometrical compass-and-straightedge constructions of an equivalent square.

- Integral1 related topic with Alpha

## Area

0 linksQuantity that expresses the extent of a region on the plane or on a curved surface.

Quantity that expresses the extent of a region on the plane or on a curved surface.

In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number.

For shapes with curved boundary, calculus is usually required to compute the area.

In addition to its obvious importance in geometry and calculus, area is related to the definition of determinants in linear algebra, and is a basic property of surfaces in differential geometry.

The development of integral calculus in the late 17th century provided tools that could subsequently be used for computing more complicated areas, such as the area of an ellipse and the surface areas of various curved three-dimensional objects.