Homework Help is Here – Start Your Trial Now!
Math
Calculus
6. Now instead, let A be the area under the graph of a decreasing continuous function f from a to b, and let L, and R be the approximations to A with n subintervals using left and right endpoints, respectively. Fill in the compound inequality, putting A, Ln, and Rn each in one blank. S Now fill in each blank with either Ln or Rn Thus, overestimates the area A and underestimates the area A. NOTE: Suppose A is the area under the graph of a function that both increases and decreases over the interval from a to b. We can't conclude that the left-hand sum would be an underestimate or an overestimate OR that the right-hand sum would be an underestimate or an overestimate. I. Estimating Area Under a Curve Suppose we want to estimate the area under the curve f(x) = x² +1 between x = 0 and x = 4. ту 16 12 8 .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 1. For the height of each rectangle, we'll use the left- hand endpoint (the height or y-value of the curve at the left side of the rectangle.) 4-0 4 =

6. Now instead, let A be the area under the graph of a decreasing continuous function f from a to b, and let L, and R be the approximations to A with n subintervals using left and right endpoints, respectively. Fill in the compound inequality, putting A, Ln, and Rn each in one blank. S Now fill in each blank with either Ln or Rn Thus, overestimates the area A and underestimates the area A. NOTE: Suppose A is the area under the graph of a function that both increases and decreases over the interval from a to b. We can't conclude that the left-hand sum would be an underestimate or an overestimate OR that the right-hand sum would be an underestimate or an overestimate. I. Estimating Area Under a Curve Suppose we want to estimate the area under the curve f(x) = x² +1 between x = 0 and x = 4. ту 16 12 8 .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 1. For the height of each rectangle, we'll use the left- hand endpoint (the height or y-value of the curve at the left side of the rectangle.) 4-0 4 =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
See similar textbooks
icon
Related questions
Question

with the example in 1st imaged attached, how can i answer question 6? 

thank you so much

6. Now instead, let A be the area under the graph of a decreasing continuous function f from a to b, and let L, and R be the approximations to A with n subintervals using left and right endpoints, respectively. Fill in the compound inequality, putting A, Ln, and Rn each in one blank. S Now fill in each blank with either Ln or Rn Thus, overestimates the area A and underestimates the area A. NOTE: Suppose A is the area under the graph of a function that both increases and decreases over the interval from a to b. We can't conclude that the left-hand sum would be an underestimate or an overestimate OR that the right-hand sum would be an underestimate or an overestimate.
Transcribed Image Text:6. Now instead, let A be the area under the graph of a decreasing continuous function f from a to b, and let L, and R be the approximations to A with n subintervals using left and right endpoints, respectively. Fill in the compound inequality, putting A, Ln, and Rn each in one blank. S Now fill in each blank with either Ln or Rn Thus, overestimates the area A and underestimates the area A. NOTE: Suppose A is the area under the graph of a function that both increases and decreases over the interval from a to b. We can't conclude that the left-hand sum would be an underestimate or an overestimate OR that the right-hand sum would be an underestimate or an overestimate.
I. Estimating Area Under a Curve Suppose we want to estimate the area under the curve f(x) = x² +1 between x = 0 and x = 4. ту 16 12 8 .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 1. For the height of each rectangle, we'll use the left- hand endpoint (the height or y-value of the curve at the left side of the rectangle.) 4-0 4 =
Transcribed Image Text:I. Estimating Area Under a Curve Suppose we want to estimate the area under the curve f(x) = x² +1 between x = 0 and x = 4. ту 16 12 8 .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 1. For the height of each rectangle, we'll use the left- hand endpoint (the height or y-value of the curve at the left side of the rectangle.) 4-0 4 =
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Functions and Change: A Modeling Approach to Coll…
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS