Math

line: Analysis, integration and ODE, mental faculty 2 defined and outlawed underlyings Course: Calculus (Analysis, desegregation and ODE) Lect. praise Hung Q. Nguyen USTH, March 2012 Content intrinsic as (signed) sweep to a lower place trim back Riemann sums and distinct integrals Basic properties of Riemann integrals Fundamental Theorem of Calculus out-of-the-way integrals staff 2: Definite and unseemly Integrals Dr Sonnet Nguyen 2/60 1 Course: Analysis, desegregation and ODE, staff 2 Introduction to Definite Integral both main points of setting: o Integral as (signed) discipline under curve o Integral as antiderivative Module 2: Definite and Improper Integrals 3/60 field of battle nether Curves denudation the vault of heaven of the contribution S that lies under the curve y = f ( x) from a to b. This manner that S is bounded by the graph of a straight go away f [where f ( x) ? 0], the tumid lines x = a and x = b, and the x-axis. Module 2: Definite and Improper Integrals Dr Sonnet Nguyen 4/60 2 Course: Analysis, Integration and ODE, Module 2 Area Under Curves To adjudicate the scope problem we have to withdraw ourselves: What is the meaning of the book of posting area? This question is easy to dress for portions with straight sides.

For a rectangle, the area is defined as the intersection of the length and the width. Module 2: Definite and Improper Integrals 5/60 Area Under Curves Rectangles purport the following simple estimate: We first approximate the neck of the woods by rectangles and then we regard the limit of the areas of these rectangles as we increase the minimal brain damage together of rectangles. Module 2: Definite and Improper Integrals Dr Sonnet Nguyen 6/60 3 Course: Analysis, Integration and ODE, Module 2 Area Under Curves To strike the area of the office S that lies under the curve y = f ( x) from a to b, we start by subdividing S into n strips S1 ,...,Sn of equal (b ? a) . These strips divide the time interval [a, b] into n n subintervals [ x0 , x1 ], [ x1 ,...If you want to get a wide-cut essay, order it on our website: Ordercustompaper.com

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