Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
1. Evaluate the following integrals involving 8(t): e4s cos(s)8(8-2) ds. (a) fe (b) S (8³+ s)8(8-2) ds. (c) S s²ln(1 + s)8(s 1) ds. (Your answer will depend on t.) -

1. Evaluate the following integrals involving 8(t): e4s cos(s)8(8-2) ds. (a) fe (b) S (8³+ s)8(8-2) ds. (c) S s²ln(1 + s)8(s 1) ds. (Your answer will depend on t.) -

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 36E
See similar textbooks
icon
Related questions
Question
100%
Note: Recall that the delta function 8(t) is the first derivative of the step function 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(8 — c) ds = i.e. the integral "picks out" the value of the function f at the location c where 8(t - c) 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: (b) 1. Evaluate the following integrals involving 8(t): (a) fe els cos(s)8(s-2) ds. S (c) [f(c), a<c<b, otherwise, [ f(s)5(s – c) ds = f(c)H(t - c). (s³ + 8)8(82) ds. Ső s² ln(1 + s)8(s 1) ds. (Your answer will depend on t.)
Transcribed Image Text:Note: Recall that the delta function 8(t) is the first derivative of the step function 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(8 — c) ds = i.e. the integral "picks out" the value of the function f at the location c where 8(t - c) 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: (b) 1. Evaluate the following integrals involving 8(t): (a) fe els cos(s)8(s-2) ds. S (c) [f(c), a<c<b, otherwise, [ f(s)5(s – c) ds = f(c)H(t - c). (s³ + 8)8(82) ds. Ső s² ln(1 + s)8(s 1) ds. (Your answer will depend on t.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS