TMJC H2 Chapter 11 Definite Integrals Learning Package 2024

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Chapter 11 Definite Integrals TMJC 2024 Page 1 of 33 H2 Mathematics (9758) Chapter 11 Definite Integrals Core Concept Notes Success Criteria: Surface Learning Deep Learning Transfer Learning  Evaluate definite integral using anti- derivatives i.e. f ( ) d F( ) F( ) b a x x a b=− , where d F( ) f ( )d xxx = (anti-derivative).  Evaluate the approximate values of definite integrals using a graphing calculator.  Interpret definite integrals as the area under a curve.  Understand that definite integral is negative when the curve is below the x-axis.  Evaluate an integrand of the form f ( )x without the use of GC.  Find the area of a region bounded by a curve and lines parallel to the coordinate axes.  Find the area of a region between a curve and a line.  Find the area of a region between two curves.  Find the volume of revolution about the x- or y-axis when it is bounded by one curve.  Explain that the area under a curve is the limit of a sum of the areas of rectangles and relate definite integral as a limit of sums i.e. 0 f ( ) d lim , b xa x x y x → =    where f ( )yx= .  Use a graphing calculator to illustrate the limiting process for simple cases.  Find the volume of revolution about the x- or y-axis when it is bounded by two curves. Definition of Learning (John Hattie): The process of developing sufficient surface knowledge to then move to deeper understanding such that one can appropriately transfer this learning to new tasks and situations.

Chapter 11 Definite Integrals TMJC 2024 Page 2 of 33 y x y = x2 1 2 §1 Definite Integral is a Process of Summation 1.1 Definite Integral as the Limit of a Sum Suppose we wish to find the area bounded by the curve 2yx= , the x-axis, the lines x = 1 and x = 2 as shown in Figure 1. Let us estimate this area by dividing it into 5, 20 and 50 equal rectangular strips as shown in the figures below and finding the total area of the rectangular strips. When n = 5 When n = 20 Total area of the rectangles = 2.04 units2 Total area of the rectangles = 2.25875 units2 1 2 y = x2 y x Figure 1 y x y = x2 O 1 2 Please watch the video in