Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
4. In this problem you will calculate x +5 dx by using the formal definition of the definite integral: п f(x) dx = lim Σ)ΔΣ %3D k=1 (a) The interval [0, 4] is divided into n equal subintervals of length Ax. What is Ax (in terms of n)? Ax= %3D (b) The right-hand endpoint of the kth subinterval is denoted x. What is X (in terms of k and n)? %3D (c) Using these choices for X and Ax, the definition tells us that 4 п x +5 dx = lim f(x)Ax 0. k=1 What is f(x)Ar (in terms of k and n)? f(x)Ax = %3D (d) Express f(x;)Ax in closed form. (Your answer will be in terms of n.) k=1 Σ k=1 (c) Using these choices for x, and Ax, the definition tells us that Σρ x² +5 dx = lim Lf)Ax 0. k=1 What is f(x)Ax (in terms of k and n)? f(x;)Ax= %3D п (d) Express f(x;)Ax in closed form. (Your answer will be in terms of n.) k=1 п Σx) Δx= %3D k=1 %3D1 (e) Finally, complete the problem by taking the limit as n ∞ of the expression that you found in the previous part. 4. п x²+5 dx%3D lim Efx;)Ax %3D -k%3D1 APR 9. tv 3D

4. In this problem you will calculate x +5 dx by using the formal definition of the definite integral: п f(x) dx = lim Σ)ΔΣ %3D k=1 (a) The interval [0, 4] is divided into n equal subintervals of length Ax. What is Ax (in terms of n)? Ax= %3D (b) The right-hand endpoint of the kth subinterval is denoted x. What is X (in terms of k and n)? %3D (c) Using these choices for X and Ax, the definition tells us that 4 п x +5 dx = lim f(x)Ax 0. k=1 What is f(x)Ar (in terms of k and n)? f(x)Ax = %3D (d) Express f(x;)Ax in closed form. (Your answer will be in terms of n.) k=1 Σ k=1 (c) Using these choices for x, and Ax, the definition tells us that Σρ x² +5 dx = lim Lf)Ax 0. k=1 What is f(x)Ax (in terms of k and n)? f(x;)Ax= %3D п (d) Express f(x;)Ax in closed form. (Your answer will be in terms of n.) k=1 п Σx) Δx= %3D k=1 %3D1 (e) Finally, complete the problem by taking the limit as n ∞ of the expression that you found in the previous part. 4. п x²+5 dx%3D lim Efx;)Ax %3D -k%3D1 APR 9. tv 3D

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
4. In this problem you will calculate x +5 dx by using the formal definition of the definite integral: п f(x) dx = lim Σ)ΔΣ %3D k=1 (a) The interval [0, 4] is divided into n equal subintervals of length Ax. What is Ax (in terms of n)? Ax= %3D (b) The right-hand endpoint of the kth subinterval is denoted x. What is X (in terms of k and n)? %3D (c) Using these choices for X and Ax, the definition tells us that 4 п x +5 dx = lim f(x)Ax 0. k=1 What is f(x)Ar (in terms of k and n)? f(x)Ax = %3D (d) Express f(x;)Ax in closed form. (Your answer will be in terms of n.) k=1 Σ k=1
Transcribed Image Text:4. In this problem you will calculate x +5 dx by using the formal definition of the definite integral: п f(x) dx = lim Σ)ΔΣ %3D k=1 (a) The interval [0, 4] is divided into n equal subintervals of length Ax. What is Ax (in terms of n)? Ax= %3D (b) The right-hand endpoint of the kth subinterval is denoted x. What is X (in terms of k and n)? %3D (c) Using these choices for X and Ax, the definition tells us that 4 п x +5 dx = lim f(x)Ax 0. k=1 What is f(x)Ar (in terms of k and n)? f(x)Ax = %3D (d) Express f(x;)Ax in closed form. (Your answer will be in terms of n.) k=1 Σ k=1
(c) Using these choices for x, and Ax, the definition tells us that Σρ x² +5 dx = lim Lf)Ax 0. k=1 What is f(x)Ax (in terms of k and n)? f(x;)Ax= %3D п (d) Express f(x;)Ax in closed form. (Your answer will be in terms of n.) k=1 п Σx) Δx= %3D k=1 %3D1 (e) Finally, complete the problem by taking the limit as n ∞ of the expression that you found in the previous part. 4. п x²+5 dx%3D lim Efx;)Ax %3D -k%3D1 APR 9. tv 3D
Transcribed Image Text:(c) Using these choices for x, and Ax, the definition tells us that Σρ x² +5 dx = lim Lf)Ax 0. k=1 What is f(x)Ax (in terms of k and n)? f(x;)Ax= %3D п (d) Express f(x;)Ax in closed form. (Your answer will be in terms of n.) k=1 п Σx) Δx= %3D k=1 %3D1 (e) Finally, complete the problem by taking the limit as n ∞ of the expression that you found in the previous part. 4. п x²+5 dx%3D lim Efx;)Ax %3D -k%3D1 APR 9. tv 3D
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 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