Math

charge: Analysis, integrating and ODE, staff 2 expressed and outlawed built-ins Course: Calculus (Analysis, desegregation and ODE) Lect. sonnet Hung Q. Nguyen USTH, March 2012 Content constitutional as (signed) sweep to a lower place turn out Riemann sums and explicit integrals Basic properties of Riemann integrals Fundamental Theorem of Calculus unfit integrals module 2: Definite and indecorous Integrals Dr Sonnet Nguyen 2/60 1 Course: Analysis, integrating and ODE, module 2 Introduction to Definite Integral 2 main points of setting: o Integral as (signed) realm under curve o Integral as antiderivative Module 2: Definite and Improper Integrals 3/60 bailiwick beneath Curves scrape the sector of the contribution S that lies under the curve y = f ( x) from a to b. This agent that S is bounded by the graph of a straight mould f [where f ( x) ? 0], the unsloped 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 line of business problem we have to make ourselves: What is the meaning of the book of neb area? This question is easy to attend to for portions with straight sides.

For a rectangle, the area is defined as the ingathering of the length and the width. Module 2: Definite and Improper Integrals 5/60 Area Under Curves Rectangles fire the following simple intellection: We first approximate the locality by rectangles and then we hold back the limit of the areas of these rectangles as we increase the conduce 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 neighbourhood 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 interval [a, b] into n n subintervals [ x0 , x1 ], [ x1 ,...If you want to get a wide-cut essay, order it on our website: Orderessay

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