Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Use the values in the table to calculate the area between g and h using left-end points for 0 ≤ x ≤ 5. X 0 1 2 3 4 5 6 f(x) g(x) h(x) 5 6 6 4 3 2 2 2122345 589 Sa 6 6 5 4 2

Use the values in the table to calculate the area between g and h using left-end points for 0 ≤ x ≤ 5. X 0 1 2 3 4 5 6 f(x) g(x) h(x) 5 6 6 4 3 2 2 2122345 589 Sa 6 6 5 4 2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
### Calculating the Area Between Functions g(x) and h(x) Using Left-End Points To find the area between the functions \( g(x) \) and \( h(x) \) for the interval \( 0 \leq x \leq 5 \), using left-end points, refer to the table values provided: #### Table of Values: | \( x \) | \( f(x) \) | \( g(x) \) | \( h(x) \) | |--------|-----------|------------|-----------| | 0 | 5 | 2 | 5 | | 1 | 6 | 1 | 6 | | 2 | 6 | 2 | 8 | | 3 | 4 | 2 | 6 | | 4 | 3 | 3 | 5 | | 5 | 2 | 4 | 4 | | 6 | 2 | 5 | 2 | ### Steps to Calculate Area: 1. **Identify the left endpoints**: Since we are using left-end points, consider the x-values at the beginning of the intervals (0, 1, 2, 3, 4). 2. **Calculate differences**: For each interval, calculate \( h(x) - g(x) \) at the left end: - At \( x = 0 \): \( h(0) - g(0) = 5 - 2 = 3 \) - At \( x = 1 \): \( h(1) - g(1) = 6 - 1 = 5 \) - At \( x = 2 \): \( h(2) - g(2) = 8 - 2 = 6 \) - At \( x = 3 \): \( h(3) - g(3) = 6 - 2 = 4 \) - At \( x = 4 \): \( h(4) - g(4) = 5 - 3 = 2 \) 3. **Calculate the area**: Sum up the differences, multiply by the width of each interval (assuming each interval is of width 1): - Total Area \( = 1 \times (3
Transcribed Image Text:### Calculating the Area Between Functions g(x) and h(x) Using Left-End Points To find the area between the functions \( g(x) \) and \( h(x) \) for the interval \( 0 \leq x \leq 5 \), using left-end points, refer to the table values provided: #### Table of Values: | \( x \) | \( f(x) \) | \( g(x) \) | \( h(x) \) | |--------|-----------|------------|-----------| | 0 | 5 | 2 | 5 | | 1 | 6 | 1 | 6 | | 2 | 6 | 2 | 8 | | 3 | 4 | 2 | 6 | | 4 | 3 | 3 | 5 | | 5 | 2 | 4 | 4 | | 6 | 2 | 5 | 2 | ### Steps to Calculate Area: 1. **Identify the left endpoints**: Since we are using left-end points, consider the x-values at the beginning of the intervals (0, 1, 2, 3, 4). 2. **Calculate differences**: For each interval, calculate \( h(x) - g(x) \) at the left end: - At \( x = 0 \): \( h(0) - g(0) = 5 - 2 = 3 \) - At \( x = 1 \): \( h(1) - g(1) = 6 - 1 = 5 \) - At \( x = 2 \): \( h(2) - g(2) = 8 - 2 = 6 \) - At \( x = 3 \): \( h(3) - g(3) = 6 - 2 = 4 \) - At \( x = 4 \): \( h(4) - g(4) = 5 - 3 = 2 \) 3. **Calculate the area**: Sum up the differences, multiply by the width of each interval (assuming each interval is of width 1): - Total Area \( = 1 \times (3
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS