02 - PPT - 6.3 Riemann Sums and Definite Integralsx - MATH 12 6.3 Riemann Sums and Definite Integrals � ∗ � � lim ∑ � � ∆ �=� �

02 - PPT - 6.3 Riemann Sums and Definite Integralsx -...

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6.3 Riemann Sums and Definite Integrals lim ? → ∞ ? = 1 ? ? ( ? ? ) ? = ? ? ? ( ? ) ?? 10/29/19 MATH 12
Lesson Objective By the end of the lesson, I will be able to… Relate Riemann sums and definite integrals
Riemann Sum The Riemann sum helps us find the area under a curve using n rectangles Height Width Where is Right hand endpoint Left hand endpoint Midpoint rule Right hand endpoint Left hand endpoint Midpoint rule # of rectangles Sum of…
Ex1. Evaluate Riemann sum for…a)taking sample points to be right hand endpoints andwith 4 rectanglesb)taking sample points to be left hand endpoints and with3 rectangles
is…
Note on integrals Area above -axis = + Area below -axis = - + - + ? 1 ? 2 ? 3
Comparing… Riemann Sum Integral If , the Riemann sum is the sum of the areas of n rectangles. If , is the area under the curve from to (using an infinite number of rectangles) .
Ex1. Express the following as integrals a) on the interval b) on the interval ? ? ? ( ? ) ?? = lim ? →∞ ? = 1 ? ? ( ? ? ) ? 2 1 1 lim [ ] 2 n i i n i x x x   2 1 1 lim [ 3 ] n i n i i x x x  
Ex3. Use the midpoint rule with… a)to approximateb)to approximate
Properties of Definite Integrals
Properties of Definite Integrals e.g.
e.g.e.g.
Properties of Definite Integrals e.g. Given 5 8 8 5 ( ) 6, ( ) 3, ( ) f x dx f x dx find f x dx
Isaac Barrow “Differentiation and integration are inverse processes”
Lesson Objective By the end of the lesson, I will be able to… Relate Riemann sums and definite integrals
Suggested Practice Page 428 # 39 – 43 (odd #s) Riemann sum and Definite Integrals worksheet #5, 6, 7, 13 Draw it first! Vocabulary: definite integral, Riemann sums, integration

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