University:
Missouri State University
Course:
MTH 261 | Analytic Geometry and Calculus I
Academic year:

2022
Views:

487

Pages:

18
Author:

Micah Williams

SECTION 6 Rectangular Approximation Methods for Area Under a Curve (Riemann Sums) How can we approximate the area under the curve using rectangles? What are the various Riemann Summation methods that can be used to approximate the area under the curve? How can Riemann sums be applied to a table of values? RECTANGULAR APPROXIMATION METHODS FOR AREA UNDER A CURVE AREA = [f(x1++ f(xn)]∆x n AREA = f(x) - Ax i=1 n = number of rectangles f(x) = length of rectangle Ax = width of rectangle Ax = (b-a) n in the interval [a, b] EXAMPLE 1: "RAM" on the Calculator Find LRAM, RRAM & MRAM with 40 rectangles to approximate the area under the curve. f(x) = x3x²+3x+2 in [2, 6] LRAM RRAM MRAM EXAMPLE 2: "RAM" on the Calculator Find LRAM, RRAM & MRAM with 100 rectangles to approximate the area under the curve. f(x) = √x+3 in [1,9] LRAM RRAM MRAM Approximations from a Table of Values Common Application. The Distance Problem 1. Suppose the odometer on our car is broken and the speedomenter readings every 5 seconds over a 30-second time interval are recorded in the table below 0 Time(s) Velocity (ft/s) 25 31 10 35 43 20 47 25 46 30 Sketch a velocity graph for the table of values, then approximate LRAM & RRAM from [0, 30). LRAM sec aeaddyufa tsec=ft RRAM Sey 5 5 10 15 202530 Seconds 05 10 5 10 15 20 30 Seconds Area-5(25)+5(31)+5(35)+5 (43) +5(47)+5(46)=1135ff Area = 5(31)+5/35)+5(43) +5(47)+5(46)+5(41) = 1215f+

Rectangular Approximation Methods for Area Under a Curve

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