What is the Fourier transform of the one-dimensional rect function rect(x) = 1, for |x| |x| < 2' for |x|>;?(requires integration)

Q: Calculate the value of the function f(x) = sinx cosx at  x= 0.1 using the 4th order derivative…

A: Suppose fx is n times differentiable function then nth degree Taylor approximation for fx near 0 as…

Q: What should be the rewrite of the integrand of (2x + 5)² dx so that the resulting integral is…

A: Topic = Integration

Q: find Fourier Sine integral of fie) fras= ol> |.

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Q: 9. Find the numerical Integration of cos(x) + sin (x) where n = 4 using trapezoidal rule.

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Q: dx x* + 1 3

A: Evaluate ∫0∞xx3+1dx=?

Q: What are the new limits of integration after applying the substitution u = 5x + z to the integral s…

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Q: Evaluate the integral dx fax √2x-x1

A: Given: I=∫dx2x-x2   As we know the common integral; ∫11-x2dx=sin-1x+C

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Q: Can we evaluate the integral of 1/(x^2+2x)^3/2 dx by using x= sec¿ - 1

A: Consider the equation

Q: 8. Evaluate x dx from the definition of RS-integral.

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Q: CSCX-1

A: Multiply numerator and denominator by (cscx-1)

Q: Evaluate a. Fв- x-3Dаx

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Q: 4) What integrals lead naturally to inverse hyperbolic functions?

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Q: Find the integral of * dx 2 sin x – cos x - |tan + 2 + v5 + C tan + 2- V5 In | tan + 2+ v5 |tan + 2…

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Q: 2. Describe how to deal with the singularity in the integral if one wants to evaluate this integral…

A: Given integral is  ∫01x-12e-x2dx           (i) Let fx=x-12e-x2 Clearly, x=0 is a singular point of…

Q: Find the indefinite integral and check the result by differentiation. dx 5 - 9x2 Part 1 of 7 (5 -…

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Q: When we find the area between an upper curve f(x) and a lower curve g(x), we integrate f(x)-g(x).…

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Q: Evaluate the integrals ∫(sec2 x) etan x dx

A: Evaluate: ∫sec2xetanxdx

Q: 4. Calculate the indefinite integrals for the following functions as integrands (section 8.3): 1 (a)…

A: See the details solution in below

Q: the point of discontinuity on(0, co), the Fourier Sine integral converges to: None (**) + f(x¯)] **)…

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Q: Find Fourier transfarm f x #1= cos aut ut

A: Given the x(t)

Q: -f integration for

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Q: In x dx 5.

A: Our Aim is to ∫ln (x)xdx -(i)

Q: When is it beneficial to use the Jacobian to change variables in a double integral?

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Q: In integrating the function fin Srdr using integration by parts, what would you choose for your de?

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Q: Why is anti-differentiation or integration important in our lives?

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Q: Only piecewise continuous functions f(x) on every finite interval (0, ∞) such that F(x)| dxis…

A: The given statement is false.

Q: f(x) = (sinx if 0 π

A: This is a question of Fourier Analysis.

Q: Integral of cos2x on [0, infinity]

A: We have to use limits to find the given integral.

Q: Find the integral of * dx J 2 sin x – cos x tan + 2 + V5 + C tan+ 2- V5 V5 |tan + 2-V5 V5 In tan+ 2+…

A: Option 2 will be correct choice.

Q: Find the area under the loop of the curve y2=x4(x+4) using integration

A: An integration formula for calculating the area under the curve will be used. We will calculate the…

Q: 4. Calculate the indefinite integrals for the following functions as integrands (section 8.3): 1 (a)…

A: Recall: ∫x2-a2 dx=12xx2-a2-12a2logx+x2-a2+C

Q: Match the integral expression on the left to an equal expression on the right. Ssin(3x)sin(4x)dx -…

A: Let's find.

Q: An even piecewise continuous function f(x) on every finite interval of (-oo, 0) such that :/ (x)|…

A: The given statement is : An even piecewise continuous function f(x) on every finite interval of -∞,∞…

Q: 4d.x To integrate the first step is to decompose the integrand to

A: Integrand is decomposed into fraction.

Q: csch (2sin 2x)dx 1. V1-4x

A: Given problem:-

Q: |x² In(x)dx

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Q: Why is that the multiplication and division of the functions cannot be used in normal integration…

A: We have to give the reason that why the multiplication and division of the functions cannot be used…

Q: What are the new limits of integration if apply the substitutior u = 6x + t to the integral sin (6x…

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Q: Prove the following continuous time Fourier transform relationship. sin(at) 1 X(N) = Continuous Time…

A: Fourier inverse of XΩ=1    -π≤Ω≤π0    otherwise is : F-1XΩ=12π∫-∞∞XΩejΩtdΩ…

Q: Sudv= 2x)dx can be evaluated using integration by parts of the form v=uv

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Q: 5. Integrate using an appropriate integration technique. a) ⌠ex sin(ex) dx b) ⌠sin3(2x) cos3(2x) dx

A: use substitution method for finding  integral

Q: Evaluate the indefinite integration. ∫?^3√(1+?^2)??

A: The indefinite integral of any function f(x)=p(q(x)) q'(x) can be evaluated using substitution of…

Q: IT Evaluate the proper integration from 0 to 4 of arctan x. Leave your answer in terms of r.

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Q: use a CAS to perform the integrations. Evaluate the integrals ∫ x ln x dx

A: A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with…

Q: 1. Find the numerical Integration of cos(x) + sin(x) where n = 4 using trapezoidal rule.

A: