Area Summations - AP Calculus - Lecture Notes, Study notes of Calculus

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Calculus Section 4.2B Notes Lea rning Targets ees 1. Evaluate area summations \5u9 ay LT: Evaluate area summations s(n) =)" fq) Ae i=i e Break the area into n rectangles e Base is Ax interval Ax = — n e Height is function value o Right-hand sum (RHS) measure height on the right “side” of the rectangle x; = start value + iAx (RHS) © Can also do LHS and MPS (mid-point) x; = start value + (i — 1)Ax (LHS) 1 x; = start value + (: -5) Ax (MPS) o Upper (circumscribed) sum: top of rectangle above function o Lower (inscribed) sum: top of rectangle below function Estimate the area under the curve. Partition into 4 subintervals. 1) y= -—2x +3; [-1,1] RHS: ox=— T= \ YO a Y a~ [4d SErCii ys a\(4) -I O Lower 7 (INSCRIBED acer ist 4 - \ N41) aes -S ‘\- 4 {ro-S0 “8 vst jet e Is this upper (circumscribed), lower (inscribed), or neither? 1/2