A)) Q1/ Find Fourier Sine Integral presentation of the function: f(x) = xe-* , x>0

Q: What is the integrable form of sin-cos-sin0 do? 2 2

A: SOLUTION-

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: A linear differential operator g D is called    annihilates the functions fx if and only if…

Q: Find the sine transform of 1 and deduce that et - eT TLX F, (cosech Tx)= 1 tanh (p/2).

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Q: What is the integrable form of sin-cos-sin0 d0? 2 2 A du B cosu du 2 -: / sinu du D du

A: Let's find.

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: Given a function f(x) = 9x+14x2-sin(2x)   To Find: A linear operator that annihilates the given…

Q: 2. Evaluate the integral / sin'at dt

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Q: Evaluate the integral f sin²(3x) cos (3x) dx.

A: The given integral is ∫sin23xcos53xdx. We have to evaluate the given integral.

Q: The trigonometric integral fs sec² x (tan³ x - 2 tan7 x) dx is equal to

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Q: Perform error analysis of approximation derived (a) 1 x² 1 - at xo = 0 X (b) sin (₁) ₁ X- at x = = 0…

A: Given that: a 1x2-1 at x0=0b sin xx-1 at x=0c exp x2-1 at x=1 and x=-1 The objective is to analyse…

Q: Determine the order of the zero at the origin of f(x) = ² (cos(z) - 1 + sin² (2))

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Q: Evaluate the integral. ∫0 π/2  Sin2 x Cos 2 x dx

A: Consider the given integral as Use the identity to solve the integral such that

Q: Evaluate the integral.  integral  sec 2 x  tan  3 x  dx

A: Consider the following integral:

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: Let D be the differential operator ddx, we have t find function f such that  fDgx=0, where…

Q: 2. F(x) = [ cosr' dt

A: Use fundamental theorem of calculus

Q: Evaluate the integral. (Use C for the constant of integration.) cos3 sin2 dt

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Q: Evaluate the definite integral 3 2 sin (2)dx using Part 1 of the Fundamental Theorem of Calculus. 57…

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Q: What is the minimum value of f(0) in the equation f(0) = 3 sin 40? %3D

A: To determine the minimum value of the below function. fθ=3sin4θ

Q: Find F'(x), where F(x)= int. of ((t^2)+1)dt, from sin(3x) to x=-4. Use the 1st rule of the…

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Q: What is the integrable form of sin-cos-sin0 de? 2 2

A: A detailed solution is given below.

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: The annihilator of a function is a differential operator which, when operated on it, obliterates it.…

Q: 5. Verify whether the function f(z) Cauchy-Riemann equations or not. sinh 4x cos 4y + i cosh 4x sin…

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Q: Use Fourier cosine transform to solve y" – y = 3e-4 y' (0) = 0 lim y (x) = 0, as x → o0

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Q: 3 4. sin x cos xdx

A: These formulae are used while solving the question:

Q: ) 3x - 4x= sin社 ; at t=0,x==

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Q: 18. Find three integrals in Exercises 39–74 that can be solvedby using a trigonometric substitution…

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Q: (ii) Hence, by using Leibniz Rule for Differentiation Under the Integral Sign, compute the value of…

A: Leibniz Rule for Differentiation under integral sign:- ∂∂t∫atbtfx, tdx=∫atbt∂f∂tdx   + fbt, t∂bt∂t-…

Q: 8 (a) To evaluate the integral J cos xdx by using the reduction formula of Cosine function.

A: We have to use cosine reduction formula.

Q: (a) Evaluate the integral sin* 4x cos3 4x dx

A: a) Evaluate the integral                                 ∫0π8 sin4 4x cos3 4x dx  Let us substitute…

Q: 2. Apply appropriate trigonometric substitution to compute the integral 1-4x +2 dx /2x

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Q: Sketch flx) = 2 cos x-Sin 2x , osx<2o

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Q: Consider - Vx2-9 x3 dx. Using trigonometric substitution, what is the integral form in terms of 0?

A: To solve a certain type of complex integrals we usually simplify them using basic trigonometric…

Q: Find Fourier sertes [o, 2] an 2) fex) f Cx) = Sin X ニ

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Q: S cos (2x) sin* (2x)dx a.

A: Solution: The objective is to evaluate the integral

Q: What is the integrable form of sin-cos-sine de? 2 2 (A) - - B -2 sinu du (D cosu du

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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: Evaluate the definite integral 27 3 16 sin (x)dx using Part 1 of the Fundamental Theorem of…

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Q: Solve the integral. cos x dx J (1+ sin² x) arctan (sin x) 10.

A: To evaluate:                      ∫cos x(1+sin2 x)arctan(sin x)dx    ... (1)

Q: Use the Intermediate Theorem show that there is a root of the given equation: sin a - x between…

A: Intermediate value Theorem states that if f is continuous on the interval (a ,b ) and L is a number…

Q: Evaluate the integral. ∫0 π/2  (2- sinθ)2dθ

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Q: Find the product of the integral ri sec²(cos(x))dxdy sin-y

A: Given ∫01∫sin-1yπ2sec2cosxdxdy

Q: What is the integrable form of sin-cos-sine de? 2 2 V1-u? du -2 sinu du u² – 1 du 2/ cosu du

A: We have given integral Let, I=∫sinθ2cosθ2sinθdθ As, sin2x=2sinxcosx sinx=2sinx2cosx2 So,…

Q: What is the integrable form of sin 0 sin-cos-sine d@? 2 2 u² – 1 du 1– u² du 2 | cosu du -2 | sinu…

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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: In (tan (x)) dx. 3. Evaluate J sin(x) cos(x)

A: NOTE: Refresh your page if you can't see any equations. . ..............(1) substitute  take…

Q: b) Evaluate the integral: S (sin-1(x))²dx

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: tan Find the integration of 1₁ 1+z²

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: The given function = 10x+ 9x2-sin6x