Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
- Evaluate the following integrals involving H(t): (a) * H(s-3) ds. 10 (b)(1-H (s-5)) ds. (c) * H(s − 1) ds. (Your answer will depend on t.) -

- Evaluate the following integrals involving H(t): (a) * H(s-3) ds. 10 (b)(1-H (s-5)) ds. (c) * H(s − 1) ds. (Your answer will depend on t.) -

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
Note: Recall that the step function H(t) is defined by Jo, t<0, | 1, t≥ 0. 1. Evaluate the following integrals involving H(t): (a) [1 H(s - 3) ds. 10 (1 - H (s - 5)) ds. › [H(s H(t) = H(s1) ds. (Your answer will depend on t.) [se Note: Recall that the delta function 8(t) is the first derivative of H(t). The key property of 8(t) is the way it behaves in integrals: for any number c and any function f, f(s)8(sc) ds = { ff(c), √ 1 (0)6(8-c a<c<b, otherwise, i.e. the integral "picks out" the value of the function f at the location c where 8(tc) has a spike. The integral is zero if the spike lies outside the domain of integration. For integrals from 0 to t, when c> 0, we can rewrite the rule more concisely with a step function: f(s)8(sc) ds = f(c)H(t-c).
Transcribed Image Text:Note: Recall that the step function H(t) is defined by Jo, t<0, | 1, t≥ 0. 1. Evaluate the following integrals involving H(t): (a) [1 H(s - 3) ds. 10 (1 - H (s - 5)) ds. › [H(s H(t) = H(s1) ds. (Your answer will depend on t.) [se Note: Recall that the delta function 8(t) is the first derivative of H(t). The key property of 8(t) is the way it behaves in integrals: for any number c and any function f, f(s)8(sc) ds = { ff(c), √ 1 (0)6(8-c a<c<b, otherwise, i.e. the integral "picks out" the value of the function f at the location c where 8(tc) has a spike. The integral is zero if the spike lies outside the domain of integration. For integrals from 0 to t, when c> 0, we can rewrite the rule more concisely with a step function: f(s)8(sc) ds = f(c)H(t-c).
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