Integrals and Derivatives

Definition

Integrals and derivatives are mathematical operations used in calculus to analyze the rate of change of a function (derivative) or find the total accumulation of a quantity over an interval (integral).

Related terms

Antiderivative: The antiderivative is the reverse operation of taking a derivative. It finds a function whose derivative is equal to a given function.

Fundamental Theorem of Calculus:

This theorem establishes the relationship between integrals and derivatives by stating that if F(x) is an antiderivative of f(x), then ∫[a,b] f(x) dx = F(b) - F(a).

Chain Rule: The chain rule is a formula used to find the derivative of composite functions. It allows us to differentiate functions within functions.