Find the Fourier integral of f(x) = e-k* when x>0 and f(-x) = f(x), hence prove that cos(wx) dw w +k? ',k >0. 2k

Q: Consider the definite integral. (8x – 1) e- dx Let u = 4x – x. Use the substitution method to…

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Q: Find the solution in the form of Fourier integrals: Ut- 3uxx = 0, u(0, t) = 0, |u(x, t) bounded as x…

A: As per the question we are given a initial boundary value problem as : ut - 3uxx = 0 And we have to…

Q: Give the general antiderivative for the integrand in the definite integral cos x + dx.

A: give the general antiderivative for the integrand in the definite integral

Q: Evaluate the double integral of cos(x) with x from 0 to π/4 and y from 4y to π

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Q: a=1 and n-1. Let f(t) = tet SHOW all of your steps of integration clearly.

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Q: By the odd extension method applied to the function f (x) = e¯2x, wherex > 0, the Fourier integral…

A: Given the function  fx=e-2x

Q: tan (In |4x2|) -dx is b in cos (In |(2x)*|)|+c. The integral of What is b?

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Q: Evaluate the iterated integral: a " cos(2) dy dar.

A: The iterated integral is given as:…

Q: 2. Evaluate the improper integral. e COs x dx

A: I=∫0∞ e-x cosx dx Integration by parts;Formula:∫(uv)dx=u∫vdx -∫dudx ∫vdx dxu=cos x, dudx=-sin…

Q: Solve the integral. 1+ In x 8. -dx J x +x In² x

A: The given integral is  I=∫1+ln(x)x+x ln2xdx The integral can be calculated by doing substitutions.

Q: what is the integral of e^(-2a|t|) from -w to w?

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Q: In 3 xp; J(1-x)*dx

A: Given,

Q: The Fourier integrals of two continuous functions f(x) and g(x) defined on R are given by = - 2n…

A: The fourier integrals of two continuous fx and gx defined on ℝ are defined…

Q: dx (1 – e²)² -1

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Q: -Find Fourier Integral for the function: f(x) = {0 x 0 0 <x < 2 1 ans: f(x) = - " sin2w cos(wx) +…

A: Given function fx=0    x&lt;0 or x&gt;01    0&lt;x&lt;2 So we must have  fx=0    x&lt;0 or x&gt;21…

Q: dx 2 -o x+4x+5

A: The general form of a complex number is given by , where a, b are two real numbers and . Any complex…

Q: Estimate the error if cos t² is approximated by 1 integral , cos r² dt. 4! in the 2

A: We have,

Q: 00 cos wx Q1/ Use Fourier Integral to show that 0. dw w2+1

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Q: Evaluate the improper intergal 1 dx using the residue (x2 + 9)* theorem.

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Q: 33. Use integration by parts to find the indefinite integral. fxcos(2x)dx -xcos(2x)–sin(2x)+c а. b.…

A: To find the integration

Q: Evaluate the improper intergal 1 dx using the residue (x² + 16)² theorem.

A: We need to evaluate integral.

Q: Consider the definite integral. (8x- – 1) e*x²-x dx Let u = 4x2 - x. Use the substitution method to…

A: Answer and explanation is given below

Q: Use Part 1 of the Fundamental Theorem of Calculus (and properties of definite integrals and the…

A: Solve the following

Q: 2. Compute the integral dy dx by interchanging the order of integration.

A: Order of change of integrals

Q: The Fourier integrals of two continuous functions f(x) and g(x) defined on R are given by sintwa] 2л…

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Q: Evaluate the integral f e² In (x²+1)dx

A: ∫e2ln(x2+1)dx

Q: At the point of discontinuity on (0, co), the Fourier Cosine integral corverges to: f(x+) – f(x¯)]…

A: We have to solve given problem:

Q: | (t – cos(3t))e-'dt

A: Using definition of Laplace transform.

Q: Which of the following integration expression can be transformed into integral of power 2 dx (A)…

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Q: dx%3D 9+x²

A: Solution is given below:

Q: Compute this improper integral showing all steps.  integral of x ln(x) dx from 0 to 2.

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Q: Evaluate the integral. 3y- cos xy dy dx x/3 O 5(1 - cos 3) O 3(1 - cos 3) O cos 3 -1 (1 cos 3)

A: Given: ∫03∫x313y2 cos xy dy dx We have x3≤y≤1 and 0≤x≤3 This can be seen as: We can change the…

Q: Evaluate the Integral dx – (**V2Tan-1x-(Tan-1x)2 1-х4 '2Tan-1x-(Тап-1x)2 3. S х?/2Tап-1x- (Тап-1x)2…

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Q: Write down the definition of the laplace transform in terms of an improper integral and use it to…

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Q: (5x° + 4x + Ix Consider the indefinite integral dx x2 – 1 Then the integrand decomposes into the…

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Q: 7. Find the indefinite integral. (a) + sec , | dx = 4 In |x| + tan(x) +C (b) / )Lanr dx = In |In x|…

A: Given that: (a)∫4x+sec2xdx(b)∫1xlnxdx(c)∫x4-3x2+5x4dx

Q: Q4: a)Evaluate the integral: ( In(cosh2x) coth2x dx b) prove that sec-1x = cos-1! = Cos

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Q: or show that the integral Integrate the following diverges: Зе In sin x ii) dx COS X 2e

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Q: Evaluate the integral. integral   sec 6  t  / tan 3t dt

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Q: Evaluate the improper intergal dx using the residue 2 (x² + 4)² theorem.

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Q: evaluate the Cauchy principal value of the given improper integral. cos 2r dx x² + 1

A: We have to find the Cauchy principal value of the improper integral. First we have to write the…

Q: Evaluate the iterated double integral JI-X² ( [√x² sin (x² + y²) dz dy dx

A: A a couple of imperative is a specific imperative of a characteristic of numerous actual variables…

Q: Evaluate the iterated integral. cos(s*) dt ds

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Q: Use Romberg integration to compute R3,3 for the following integral cos x dx

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Q: Consider the definite integral. (18x – 1) e9x²-x dx Let u = 9x? - x. Use the substitution method to…

A: We have to find the integrand after substitution.

Q: Use Romberg integration to compute R3,3 for the following integral x cos x dx

A: Romberg integration is one of the way to approximate the value of definite integrals. In this…

Q: Evaluate Poisson Integral: In(1-2a cos(x) + a²) dx ,a.) [a| 1,

A: To evaluate Poisson's integral: ∫0πln1-2αcos(x)+α2dx  a)α&lt;1 b)α&gt;1

Q: Use the integration theorem to show that Cos nx 효(72-3a2) =D Σ(-1)”-1! -T <x < T n2 n=1 and sin nx…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Calculate the gaussian integral, e- dx, using the complex integration [residue theorem]

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Q: By the odd extension method applied to the function f(x) = e-2=, where a > 0, the Fourier integral…

A: The given function is, f(x)=e-2x,x&gt;0