Unit 6: Integration and Accumulation of Change

Integral

Also called the antiderivative, it shows the total change of a function.

Definite Integral

Represents the area under a function and above the x-axis, giving total accumulation/change.

Riemann Sum

A method to estimate the area under a curve by dividing it into rectangles.

Trapezoidal Sum

An estimation that uses trapezoids instead of rectangles to better fit the shape of the curve.

Fundamental Theorem of Calculus

States that the integral from a to b equals the antiderivative evaluated at b minus the antiderivative evaluated at a.

Antiderivative

The reverse process of differentiation, leading to the original function from its derivative.

Power Rule

A rule used in integration, where we increase the power by one and divide by the new power.

Constant of Integration (C)

Added to the antiderivative to account for unknown constants when reversing differentiation.

U-Substitution

A technique used in integration to simplify the process by substituting a variable.

Midpoint Sum

A method to estimate the area under the curve by using the heights from the midpoints of intervals.

Left Endpoint Sum

A method to estimate the area under the curve by using the heights from the left endpoints of intervals.

Right Endpoint Sum

A method to estimate the area under the curve by using the heights from the right endpoints of intervals.