Integral calculus

Definition

Integral calculus is a branch of calculus concerned with the accumulation of quantities and the areas under and between curves. It focuses on integrals, including definite and indefinite integrals.

5 Must Know Facts For Your Next Test

1. The fundamental theorem of calculus links differentiation and integration.
2. A definite integral calculates the net area under a curve within a given interval.
3. An indefinite integral represents a family of functions whose derivative is the integrand.
4. Integration can be used to find areas, volumes, central points, and many useful things.
5. Common techniques for evaluating integrals include substitution and integration by parts.

Review Questions

• What does the fundamental theorem of calculus state about differentiation and integration?
• How does a definite integral differ from an indefinite integral?
• What are some common techniques used to evaluate integrals?

Related terms

Derivative: A measure of how a function changes as its input changes; it represents an instantaneous rate of change.

Fundamental Theorem of Calculus:

A principle that links the concept of differentiating a function with that of integrating a function.

Antiderivative: A function whose derivative is the original function; also known as an indefinite integral.