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(a) Solve the following integrals: ed 2t (i). s dt +1 (ii). ſe * sin x...
3- Solve the following improper integrals 1="e 'dt 4- Solve the following improper integrals I
Please answer all three parts.
(i) Take the laplace transform with respect to t
(ii) Solve the resultant integral in x
(iii) Solve the result from s-space to t-space using the
Bromwich integral
2. Obtain these integrals by (i) taking the Laplace transform w.r.t. t, (ii) solving the resultant integral in I, and then (iii) inverting the result from s-space to t-space using the Bromwich integral (b) g(t) = po sin(t I) de (12+1)
(i) Write down the mathematical definition of the Dirac delta function. (ii) Compute the following integrals | ** cos(e)8(t – 2) dt f sin®(t + 7/3)8'(t) dt e '8(t? – r) dt where x is a real non-zero number.
Evaluate the following integrals (from A to E) A. Integration by parts i) ſ (3+ ++2) sin(2t) dt ii) Z dz un (ricos x?cos 4x dx wja iv) (2 + 5x)eš dr. B. Involving Trigonometric functions 271 п i) | sin? ({x)cos*(xx) dx ii) Sco -> (=w) sins (įw) iii) sec iv) ſ tan” (63)sec^® (6x) dx . sec" (3y)tan?(3y)dy C. Involving Partial fractions 4 z? + 2z + 3 1) $77 dx 10 S2-6922+4) dz x2 + 5x -...
Find the following integrals using integration by parts (IBP)
(e) cos'(t)dt (f) S[In(t)]?dt (g) 83" 02 sin(20)de
(1 point) Solve the system 4 -2 dx II dt 10 -4 -3 with x(0) = -2 Give your solution in real form. Xı = -3cos(21)+(27sin(2t))/5 x2 = -2cos(2t)-11 sin(2t) An ellipse with counterclockwise orientation 1. Describe the trajectory.
please complete all parts
Problem F.7: These are independent problems (a) (5 points) Solve the following integral. (Hint: Think Fourier series.) (cos(nt) - 2sin(5rt)e-Jr dt XCj) (b) (5 points) Find the Fourier transform io of the following signal: 2(t) = sin(4t)sin(30) (c) (5 points) Solve the integral: sin(2t) 4t dt (d) (5 points) Use Parseval's theorem and your Fourier transform table to compute this integral:
Problem F.7: These are independent problems (a) (5 points) Solve the following integral. (Hint: Think...
Please solve the all questions. Thanks
Probleml: Suppose that F(x) = $ f (Ed dt, where ! Find "(2). Carral Problen 2: Let y = f Use the fundamental Theoren 10t+ sin(tl) at of Calculus to find. using the fundamentul Find the derivative of the function Theoren of Calculus. F(x) = f (2 2-2) de Find & flxd dx if ft) = { t for I for X21. r for x> 1. z
1: Evaluate the following integral. Hint: (Use definition of Laplace transform. No need to integrate) i./el1-s)t sin(3+)dt. ii. [ -st (83 + cos(2t)dt.
please simplify
Problem 2.3 Evaluate or simplify the following integrals or expression as much as possible (show your work). (a) L, 8(t)x(t – 1)dt (e) , 8(at)dt (i) cos(10zt) [8(t) + 8(t + 5)] sin (b) 8(t – T)x(t)dt (f) 8(2t – 5) sin nt dt (c) L 8(t)x(r – t)dt cos (x - 5)|6(x – 3)dx (sin ke (B) e*-2 8(w) (k) 6(r – t)x(t)dt (d) (h) Jt-11 t+9 8(1 – 3)đr Problem 2.3 Evaluate or simplify the following...