Change variables under the Laplace integral to prove that for a fixed τ,
L{x(t−τ)}=e^(−sτ) X(s)
Change variables under the Laplace integral to prove that for a fixed τ, L{x(t−τ)}=e^(−sτ) X(s)
Use the Laplace transform to solve the given integral equation. f(t) + t (t − τ)f(τ)dτ 0 = t
4. Use the Laplace integral formula to find (b) L-1 T"e (5-1) s2(s 1) 0 4. Use the Laplace integral formula to find (b) L-1 T"e (5-1) s2(s 1) 0
7.1: Definition of Laplace transform 17. Prove L {eat f(t)} = F(s – a) 18. Prove L {f'(t)} = sF(s) – f(0)
3. Solve the following integral equations using Laplace transforms. (a) (t)= te! - 2e x(u)e"du (b) y(t) 1 - sinht +(1+T)y(t - T)dT. netions 3. Solve the following integral equations using Laplace transforms. (a) (t)= te! - 2e x(u)e"du (b) y(t) 1 - sinht +(1+T)y(t - T)dT. netions
Use a change of variables to evaluate the following definite integral. 0 S xV81-x* dx -3 Determine a change of variables from x to u. Choose the correct answer below. O A. u=x4 O B. u = 81- x4 O C. u = 4x3 OD. u= 181 - x4 Write the integral in terms of u. S xV81-x* dx= du -3 Evaluate the integral. 0 5 x 181-x* dx= { -3 (Type an exact answer.)
Question 5: Prove the following: a) Theorem 5.1: If then Page 3 of 8 te, 2017 SEE307 Systems and Signals Trimester 1, 2017 1Uw).su»-1 {Lh(thu-thar} = F(s)Kfs) where L(.) represents the Laplace transform. (15 marks) b) The output ) of an analog averager is given by which corresponds to the accumulation of values of x() in a segment [t-T.r]divided by its length T, or the average of x(0) in [t-T,1]. Use the convolution integral to find the response of the...
USE DEFINITION 1 TO DETERMINE THE LAPLACE TRANSFORM OF THE FOLLOWING FUNCTION. f(t)= e sin(t) Laplace Transform Definition 1. Let f(t)be a function on [0,00). The Laplace transform of f is the function defined by the integral The domain of F(s) is all the values of " for which the integral in (1) exists.' The Laplace transform of fis denoted by both and ${/}. QUESTION 2. (3PTS) USE TABLE 7.1 AND 7.2 TO DETERMINE THE LAPLACE TRANSFORM OF THE GIVEN...
3. Using the properties of Laplace transforms, prove that L {e^!} = (sI – A)?. ****
Integral Transform Use the definition of Laplace transform to approve L{t} = 1/s2.
Use the given change of variables to evaluate the integral. 2 R Sja (x + y)e=* DA R R is the region enclosed by y = 1, y = 2-2, y=-1, y = -2+3 Su= x - y v=x+y