I have all parts solved except part c where I am confused on how to evaluate the integral a. Set up an integral for finding the Laplace transform of the following function:0

Answered: Image /qna-images/answer/e2c50ffb-3cfd-4988-82d7-4fbb101fdfe9.jpg

Answered: a. Set up an integral for finding the…

Math

Advanced Math

a. Set up an integral for finding the Laplace transform of the following function: { 0, li+1, 0

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

Related questions

Q: 3. f(t) = t°e^(-4t) 4. f(t) = (e^(10t)) sin(2t)

Q: Determine the initial value of c(t) where the Laplace transform of C(s) is given by: (4s +1) s(s +…

Q: Use the Laplace transform to solve the given initial value problem. For technical reasons, write u…

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" -…

Q: 1. Use the Laplace transform to solve the given initial-value problem. (1, 0st< sint, t2 y" + y =…

A: Given : The initial value problem y''+y=f(t) , y(0)=1, y'(0)=0, where f (t) = 1 , 0…

Q: 1. A) Evaluate the integral fe"(1+t sinf)dt by using Laplace transform definition and properties of…

Q: Q5. Find the Laplace Transform of the funetions x(t) and yıt), which satisfy the coupled first…

Q: 1. a) Find the Laplace transform for the functions below. (i) f(t)= e²¹ sin(not), n integer. (ii)…

Q: 3. Using Laplace Transform Solve d'y dy = sint, given that y =! dy =0 when t=0 +2 - 3y dr? dt dt

A: The given problem is to solve the given initial value problem with given initial conditions using…

Q: Consider the following initial value problem, in which an input of large amplitude and short…

Q: L[t e-t sin 3t dt ]

Q: Consider the following initial value problem, in which an input of large amplitude and short…

A: Inverse Laplace transferom

Q: Consider the following initial value problem, in which an input of large amplitude and short…

Q: a) Consider the following function UTM UT Cos t, cos 2t, 0 T. UTM ii. Hence, find its Laplace…

A: The given problem is to express the given function in terms of unit step function and also find the…

Q: 8. Express the given function using unit step functions and compute its Laplace transform y sin t N…

Q: 1. A) Evaluate the integral (e*(1+t sint)dt by using Laplace transform definition and properties of…

Q: Use the Laplace transform to solve the given initial value problem. For technical reasons, write uç…

Q: 10) Use the Laplace transform to solve the given initial-value problem. y'-y = 2 cos (3t) when y(0)…

Q: Consider the following initial value problem, in which an input of large amplitude and short…

A: Given the differential equation x''+4π2x=2πδt-1 with initial conditions x(0)=0, x'(0)=0.…

Q: B: The Laplace transform of the; f(t) = e-t.sinh 3t

A: # we are entitled to solve one question at a time , please resubmit the other question if you wish…

Q: Q1 (a): Use the Laplace transform method to solve generalized Abel integral equation u(t) dt , f(x)…

A: Given :- Use the Laplace transform method to solve generalised Abel integral equation, fx = ∫0τ…

Q: 10. Use the method of Laplace transform to solve the initial value problem y" – 2ay + (a? + B²)y =…

Q: 1 Prove that L(sinh t) %3D (s2–1)

Q: a"(t) + 16x(t) = 5 sin t, a'(0) = x(0) = 0 %3D

A: First we have to take Laplace transform of the given equation.

Q: Use the Laplace transform to solve the given initial-value problem. y"+y= (t-극) + 이t-), y(0)= 0,…

A: The Laplace transform is an integral transform that converts a function of a real variable t to a…

Q: Find the Laplace transform of the following differential equation : * + 2x + 17x = 0 x(0) = 0, ¿(0)…

Q: Use the Laplace transform to solve the given initial-value problem. y"+y-d(t-글) + o(t-) y(o)-0,…

Q: a) Solve the initial value problem using Laplace transform TM UTM® y' + 2y = 26 sin 3t, y(0) = 3.…

A: The differential equation is given as y'+2y=26 sin3t and the initial condition is y(0)=3 Use the…

Q: Consider the following initial value problem, in which an input of large amplitude and short…

A: Given, x''-6x'=δ(t-4), x(0)=7, x'(0)=0. a). We know that,…

Q: 1. Find the inverse Laplace transform of the function 2/ s (s + 1) with the help of convolution.

A: 2-2e^(-t)

Q: By using Laplace transform to solve y"-y e' with y (0) = 1 and y (0) = 0 ,what would the particular…

Q: Use the Laplace Transform method to solve the following IVP. y" - 2y + y = cos(t), y(0) = 1, y'(0) =…

Q: Use the Laplace transform to solve the given initial value problem. y" - 2y' + 2y = cos t; y(0) = 1,…

A: The differential equation is given as : y''-2y'+2y=cos ty(0)=1y'(0)=0 The objective is to find the…

Q: (i) Find the Laplace transform of e" sin 21 dt (ii) Form the PDE by eliminating arbitrary constants…

Q: Consider the following initial value problem, in which an input of large amplitude and short…

A: Given differential equation is,x1+x=4+δ(t-1) , x(0)=0 -(1)We know that,L{x'(t)} =L{x(t)}-…

Q: Prove by conventional integration that the Laplace transform of the given function is equal to the…

Q: 2. Use Laplace transform to solve with y (0) y" + 4y = 8(t)- 8(t - 2π) 0 and y' (0) = 0.

Q: Use the Laplace transform to solve the given initial-value problem dy --y=1, dt y(0)=0 Select one: O…

Q: 2. Use Laplace transform to solve with y(0) = y" + 4y = = 8(t)- 8(t - 2π) 0 and y' (0) = 0.

Q: Let us find the Laplace transform of u(t-a), where a 2 0 is some constant. That is, the function…

A: Here we have to compute the laplace transform of u(t-a)

Q: 7) Use the Laplace transform method to solve the Volterra integral equation: u (x ) = 1-x - (x –t )u…

Q: By using Laplace transform to solve y' +4y +8y = sint with y (0) = 1 and y (0) = 0, what would be…

Q: Solve the DE y" + 2y' + y = 0 using Laplace Transform when y(0) = -1 y'(0) = 1. Evaluate f (0)

Q: Consider the following initial value problem, in which an input of large amplitude and short…

A: According to the given information, it is required to solve the initial value problem using laplace…

Question

I have all parts solved except part c where I am confused on how to evaluate the integral

a. Set up an integral for finding the Laplace transform of the following function:
0 <t < 6
6 <t.
0,
f(
F() = { .
t+ 1,
В
F(s) = L {f(t)} =
e^(-st)(t+1)dt
help (formulas)
where A =
6.
and B =
inf
b. Find the antiderivative (with constant term 0) corresponding to the previous part.
(-t/s)e^(-st)-(1/s^(2)e^(-st))-(1/s)e^(-st)
c. Evaluate appropriate limits to compute the Laplace transform of f(t):
F(s) = L {f(t)} = (6/s)e^(-6s)+(1/s^(2))e^(-6s)
d. Where does the Laplace transform you found exist? In other words, what is the domain of F(s)?
(0,inf)
help (inequalities)

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Indefinite Integral$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated