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Course: Analysis, desegregation and ODE, Module 2 certain(prenominal) and outlawed Integrals Course: Calculus (Analysis, desegregation and ODE) Lect. Sonnet Hung Q. Nguyen USTH, March 2012 satisfy Integral as (signed) sweep to a lower direct burn Riemann sums and definite integrals Basic properties of Riemann integrals Fundamental Theorem of Calculus unlawful integrals Module 2: Definite and Improper Integrals Dr Sonnet Nguyen 2/60 1 Course: Analysis, Integration and ODE, Module 2 Introduction to Definite Integral Two main points of screen background: o Integral as (signed) area under curve o Integral as antiderivative Module 2: Definite and Improper Integrals 3/60 Area nether Curves remark the area of the contribution S that lies under the curve y = f ( x) from a to b. This means that S is bounded by the graph of a straight function f [where f ( x) ? 0], the vertical lines x = a and x = b, and the x-axi s. 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 area problem we have to ask ourselves: What is the convey of the book of account area? This question is easy to coiffe for portions with straight sides.

For a rectangle, the area is defined as the fruit of the length and the width. Module 2: Definite and Improper Integrals 5/60 Area Under Curves Rectangles suggest the following simple idea: We first approximate the region by rectangles and accordingly we take the limit of th e areas of these rectangles as we increase ! the add 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 region S that lies under the curve y = f ( x) from a to b, we dinero by subdividing S into n strips S1 ,...,Sn of equal (b ? a) . These strips divide the separation [a, b] into n n subintervals [ x0 , x1 ], [ x1 ,...If you want to get a wide-eyed essay, order it on our website: BestEssayCheap.com

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