integral calculus

Thân thiện

A student solves a problem using integral calculus on a chalkboard.

Definition

Noun: The branch of calculus concerned with integration and its applications. This includes finding integrals, which are the mathematical objects that describe accumulation of quantities (such as areas under curves, volumes, total displacement) and provide solutions to differential equations.

Usage

Integral calculus is used as a singular noun to refer to this specific mathematical discipline. It is often contrasted with its counterpart, differential calculus. - Example: A strong understanding of both differential and integral calculus is essential for engineering students. - Example: The problem of finding the area under a parabola is solved using integral calculus.

Advanced Usage

• "The fundamental theorem of integral calculus": This is a core principle linking differential and integral calculus, stating that differentiation and integration are inverse operations.
• Applied integral calculus: Refers to the use of integration techniques to solve practical problems in physics, economics, and other fields.

Variants and Related Words

• Integral (noun/adjective): As a noun, it refers to the result of an integration operation (e.g., "Solve the integral."). As an adjective, it means necessary to make a whole complete (e.g., "an integral part").
• Integration (noun): The process of finding an integral; the core operation of integral calculus.
• Integrate (verb): To perform the mathematical operation of integration.

Synonyms

• None that are exact. The concept is uniquely defined within mathematics. Related fields include mathematical analysis and infinitesimal calculus (which encompasses both differential and integral calculus).

Related Phrases

• "Techniques of integration": The various methods (like substitution, integration by parts) used in integral calculus to find integrals.
• "Definite/indefinite integral": Key concepts within integral calculus. A definite integral computes a numerical value (like an area), while an indefinite integral finds a family of functions (the antiderivative).

Related Idioms

No idioms are directly associated with this specific technical term.

Học thuật

Noun

1. the part of calculus that deals with integration and its application in the solution of differential equations and in determining areas or volumes etc.