IndietroFundamental Theorem of Calculus definitions
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1/15IndietroSkip to main contentIndietroDefinite Integral
Represents the signed area under a curve between two bounds, calculated using antiderivatives and subtraction. Antiderivative
A function whose derivative returns the original function, used to evaluate definite integrals efficiently. Continuity
A property ensuring a function has no breaks or jumps on an interval, required for applying the theorem. Interval
A set of real numbers between two endpoints, often serving as the bounds for integration. Upper Bound
The highest value in the limits of integration, where the antiderivative is evaluated and subtracted. Lower Bound
The lowest value in the limits of integration, used as the starting point for evaluating the antiderivative. Chain Rule
A differentiation technique applied when the upper bound of an integral is a function of the variable. Power Rule
A method for finding antiderivatives or derivatives involving exponents, crucial for integration steps. Variable Substitution
The process of replacing the variable inside an integral with the upper bound during differentiation. Signed Area
The net area under a curve, accounting for regions above and below the x-axis, found using definite integrals. Plus C
The constant of integration, omitted in definite integrals since it cancels during subtraction of bounds. Bar Notation
A vertical line indicating evaluation of an antiderivative at the upper and lower bounds. Function of x
An expression where the variable x determines the output, often used as the upper bound in integrals. Derivative
A measure of how a function changes as its input changes, central to connecting integrals and antiderivatives. Cancellation
The phenomenon where differentiation and integration undo each other, yielding the original function.
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