integral

Belonging to something as a necessary part that cannot easily be removed.

• Music is an integral part of the show.
• These checks are integral to the process.
• The handle is integral to the lid and cannot be removed.

How to use it: integral to something (Trust is integral to a good friendship.)

Similar words: essential, necessary, built-in

Opposites: inessential

Common phrases: integral part, integral component, integral to something, integral element

The number or expression found by adding up infinitely many very small amounts in calculus.

• The integral equals zero.
• We calculated the integral over the given interval.
• This definite integral gives the area under the curve.

How to use it: integral of a function (The integral of this function over that interval equals four.)

Common phrases: definite integral, evaluate an integral, integral of something

A calculus operation that adds infinitely many very small amounts to find areas, volumes, or totals.

• Use an integral to find the area.
• The integral combines the small changes into a total.
• A double integral can be used to calculate volume.

How to use it: integral with respect to a variable (Take the integral with respect to time.)

Similar words: integration

Common phrases: take an integral, double integral, integral sign, integral of something