뒤로Substitution definitions
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1/15뒤로Skip to main content뒤로Composite Function
An expression where one function is nested inside another, often seen as f(g(x)), requiring special integration techniques. Chain Rule
A differentiation method for composite functions, whose reverse process inspires substitution in integration. Substitution
A technique for simplifying integrals by replacing a complex expression with a single variable, often called u. U-Substitution
A specific substitution method where a new variable u replaces an inner function, streamlining integration. Change of Variables
A process of rewriting an integral in terms of a new variable to simplify evaluation, especially for composite functions. Definite Integral
An integral with upper and lower bounds, representing the net area under a curve between two points. Indefinite Integral
An integral without bounds, representing a family of antiderivatives plus a constant of integration. Bounds
The limits of integration in a definite integral, which may be transformed during substitution. Antiderivative
A function whose derivative yields the original integrand, found during the integration process. Power Rule
A rule for integrating or differentiating expressions with exponents, crucial for evaluating polynomials. Constant of Integration
An arbitrary constant added to indefinite integrals, accounting for all possible antiderivatives. Reciprocal
A value that, when multiplied by a given number, yields one; used to adjust constants during substitution. Fundamental Theorem of Calculus
A principle linking differentiation and integration, allowing evaluation of definite integrals using antiderivatives. Placeholder Variable
A temporary symbol, such as u, used to simplify expressions during substitution before reverting to the original variable. Derivative
A measure of how a function changes as its input changes, used to find du when making a substitution.
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