Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Consider the given function. f(x) = c +8 Evaluate the Riemann sum for 0 ≤ x ≤ 2, with n = 4, correct to six decimal places, taking the sample points to be midpoints. Part 1 of 3 We must calculate M4= Since we wish to estimate the area over the interval [0, 2] using 4 rectangles of equal widths, then each rectangle will have width Ax= -1/2 X Part 2 of 3 We wish to find M4= x₂ = Since X₁, X₂, x3, x4 represent the midpoints of the four sub-intervals of [0, 2], then we must have the following. X1 0.25 1/4 x3 X4 = · Ĺ ‹(ׂ)µ× = [r(×₁) + f(×₂) + √(×3) + f(xa)]µ×, where X₁, X₂, X3, X4 represent the midpoints of four equal sub-intervals of [0, 2]. /=1 = (±)[^(×₁) + f(×₂) + √(×3) + f(×4)] · M4 = 0.75 ✔ 1.25 1.75✔ 3/4 5/4 7/4 Part 3 of 3 Using f(x) = ex + 8, we have the following. · ( ² ) [( ₁ + ₁) + (² + •)· ( √ - · 8) + (∞— + 8) + ( ∞ — + s)] (rounded to six decimal places) 1/2.

Consider the given function. f(x) = c +8 Evaluate the Riemann sum for 0 ≤ x ≤ 2, with n = 4, correct to six decimal places, taking the sample points to be midpoints. Part 1 of 3 We must calculate M4= Since we wish to estimate the area over the interval [0, 2] using 4 rectangles of equal widths, then each rectangle will have width Ax= -1/2 X Part 2 of 3 We wish to find M4= x₂ = Since X₁, X₂, x3, x4 represent the midpoints of the four sub-intervals of [0, 2], then we must have the following. X1 0.25 1/4 x3 X4 = · Ĺ ‹(ׂ)µ× = [r(×₁) + f(×₂) + √(×3) + f(xa)]µ×, where X₁, X₂, X3, X4 represent the midpoints of four equal sub-intervals of [0, 2]. /=1 = (±)[^(×₁) + f(×₂) + √(×3) + f(×4)] · M4 = 0.75 ✔ 1.25 1.75✔ 3/4 5/4 7/4 Part 3 of 3 Using f(x) = ex + 8, we have the following. · ( ² ) [( ₁ + ₁) + (² + •)· ( √ - · 8) + (∞— + 8) + ( ∞ — + s)] (rounded to six decimal places) 1/2.

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
Tutorial Exercise Consider the given function. f(x) = e² +8 Evaluate the Riemann sum for 0 ≤ x ≤ 2, with n = 4, correct to six decimal places, taking the sample points to be midpoints. Part 1 of 3 We must calculate M₁ = Since we wish to estimate the area over the interval [0, 2] using 4 rectangles of equal widths, then each rectangle will have width Ax = -1/2 X - Σ ‹(×;)µ× = [√(x1) + √(×2) + √(×3) + f(xa)]µ×, where X₁, X2, X3 X4 represent the midpoints of four equal sub-intervals of [0, 2]. Part 2 of 3 We wish to find M4 = (¹)[(1) + t(×2) + f(×3) + f(×4)]· Since X₁, X2, X3, X4 represent the midpoints of the four sub-intervals of [0, 2], then we must have the following. X₁ = 0.25✔✔ 1/4 X2 = 0.75 ✔✔ x3 = 1.25 ✔ X4 = 1.75 ✔ 3/4 5/4 7/4 Part 3 of 3 Using f(x) = ex + 8, we have the following. M₁ - (+)(d M4 +8 ³+ 8) + (₁+3)+(₁+3)] (rounded to six decimal places) Submit Skip (you cannot come back) 1/2.
Transcribed Image Text:Tutorial Exercise Consider the given function. f(x) = e² +8 Evaluate the Riemann sum for 0 ≤ x ≤ 2, with n = 4, correct to six decimal places, taking the sample points to be midpoints. Part 1 of 3 We must calculate M₁ = Since we wish to estimate the area over the interval [0, 2] using 4 rectangles of equal widths, then each rectangle will have width Ax = -1/2 X - Σ ‹(×;)µ× = [√(x1) + √(×2) + √(×3) + f(xa)]µ×, where X₁, X2, X3 X4 represent the midpoints of four equal sub-intervals of [0, 2]. Part 2 of 3 We wish to find M4 = (¹)[(1) + t(×2) + f(×3) + f(×4)]· Since X₁, X2, X3, X4 represent the midpoints of the four sub-intervals of [0, 2], then we must have the following. X₁ = 0.25✔✔ 1/4 X2 = 0.75 ✔✔ x3 = 1.25 ✔ X4 = 1.75 ✔ 3/4 5/4 7/4 Part 3 of 3 Using f(x) = ex + 8, we have the following. M₁ - (+)(d M4 +8 ³+ 8) + (₁+3)+(₁+3)] (rounded to six decimal places) Submit Skip (you cannot come back) 1/2.
Expert Solution
steps

Step by step

Solved in 3 steps with 14 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