MATH 31A Midterm: Math 31A Exam 11
Document Summary
The nal is cumulative but will not include prob- lems about limits, curve sketching and riemann sums. More information about what we covered can be found in the previous midterm reviews. This review will only cover the material after the second midterm (i. e. , in- tegration). If we want to approximate an area we can slice it into little strips each of which can be approximated by a rectangle; we then add up the individual rectan- gles. To get a better approximation we can make the slices smaller . This is the underlying idea of rie- mann sums. Given a function f (x) and an interval. [a, b] we start by partitioning [a, b] up into a partition into pieces by rst choosing points. Properties of integration follow from the de nition of riemann sums (as well as some geometric intuition). Z b a f (x) dx = (cid:20) area above x-axis (cid:21) (cid:20) area below x-axis (cid:21).
