MATH-M 211 Lecture Notes - Lecture 20: Antiderivative, Riemann Sum
Document Summary
Section 4. 3 notes- riemann sums and definite integrals. All other rectangles smaller than infinitely small biggest rectangle. General partition- norm related to number of subintervals; norm of partition approaches 0, number of subintervals approaches ; Definite integral- if is defined on closed interval [a, b] and limit of riemann sums over partitions exists, then is said to be integrable on [a, b] and the limit is denoted by. Limit called definite integral of from a to b. Number a is lower limit of integration. Number b is upper limit of integration. Theorem 4. 4- continuity implies integrability: if a function is continuous on closed interval [a, b], then is integrable on [a, b, if continuous, exists. Theorem 4. 5- definite integral as area of a region: if is continuous and nonnegative on closed interval [a, b], then area of region bounded by graph of , the x-axis, and the vertical lines and is given by.
