AP Calculus AB - Approximating Area Using Riemann Sums

Flashcards for AP Calculus AB Quiz 1 - Topic 6.2: Approximating Area Using Riemann Sums

Right Riemann Sum (AR)

Approximation of the area under a curve using rectangles where the height of each rectangle is determined by the function's value at the right endpoint of the subinterval.

Left Riemann Sum (AL)

Approximation of the area under a curve using rectangles where the height of each rectangle is determined by the function's value at the left endpoint of the subinterval.

Trapezoidal Sum

Approximation of the area under a curve using trapezoids. It averages the left and right Riemann sums.

Relationship between Ln, Tn, and Rn (decreasing, concave down function)

For a positive, continuous, decreasing, and concave down function, the relationship is T < R < L.

Midpoint Rule

Approximates the definite integral of a function by using a Riemann sum where the height is the value of the function at the midpoint of each subinterval.

Area approximation with velocity

The area under a velocity-time curve represents the distance traveled.