I. Estimating Area Under a Curve Suppose we want to estimate the area under the curve f(x) = x² + 1 between x = O and x = 4. y 16 f. Now draw the rectangles for Rg and SHADE INSIDE EACH RECTANGLE. ΤΥ 16 12 8 12 CO .5 1.0 1.5 2.0 2.5 3.0 3.5 .5 1.0 1.5 2.0 2.5 3.0 3.5 To find the shaded area, we will use Riemann rectangles (named for Bernard Riemann). Suppose we draw 4 rectangles to estimate the area under the curve using a left-hand sum. We break up our horizontal distance into 4 equal lengths. We take the total width, 4 - 0 = 4, and divide it by the number of rectangles, 4, to get equal-width rectangles. Thus, each rectangle is width 440 = 1. For the height of each rectangle, we'll use the left- 4 hand endpoint (the height or y-value of the curve at the left side of the rectangle.) g. Now estimate the area under the curve between x = 0 and x = 4. Show your set-up like you did in part (d) and put your final answer in the second blank. Use the function formula to calculate the y-values. Estimating from the graph is not accurate enough. R8: R8: = = (Area)

I. Estimating Area Under a Curve Suppose we want to estimate the area under the curve f(x) = x² + 1 between x = O and x = 4. y 16 f. Now draw the rectangles for Rg and SHADE INSIDE EACH RECTANGLE. ΤΥ 16 12 8 12 CO .5 1.0 1.5 2.0 2.5 3.0 3.5 .5 1.0 1.5 2.0 2.5 3.0 3.5 To find the shaded area, we will use Riemann rectangles (named for Bernard Riemann). Suppose we draw 4 rectangles to estimate the area under the curve using a left-hand sum. We break up our horizontal distance into 4 equal lengths. We take the total width, 4 - 0 = 4, and divide it by the number of rectangles, 4, to get equal-width rectangles. Thus, each rectangle is width 440 = 1. For the height of each rectangle, we'll use the left- 4 hand endpoint (the height or y-value of the curve at the left side of the rectangle.) g. Now estimate the area under the curve between x = 0 and x = 4. Show your set-up like you did in part (d) and put your final answer in the second blank. Use the function formula to calculate the y-values. Estimating from the graph is not accurate enough. R8: R8: = = (Area)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.3: Trigonometric Functions Of Real Numbers

Problem 67E

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