Accumulation of change and Riemann sums

Learning objectives

Interpret the area between the graph of a rate of change and the horizontal axis as the net change in the quantity, with area below the axis counted as negative, and give the units of an accumulated quantity

Approximate a definite integral using left, right and midpoint Riemann sums and trapezoidal sums with equal or unequal subintervals, from a formula, a table of values or a graph

Decide whether a given approximation is an overestimate or an underestimate from whether the function is increasing or decreasing, or concave up or concave down, and justify the answer

Write a Riemann sum in sigma notation and define the definite integral as the limit of Riemann sums as the number of subintervals tends to infinity

Convert between a limit of a Riemann sum and the definite integral it represents, identifying the integrand, the interval of integration and the width Δx