By the even extension method applied to the function f (x) = e-2", where x > 0, the value of the integral / 00 cos(9w) dw = 4 + w2

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A: ∫cosy21-siny dy

Q: B) Use the techniques of integration to evaluate. (Solve 2 only) 3) J tan-ty dy dx 2) (1– x²)5

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Q: ⌠31 (e0.5x + sin2x) dx. use n=4 ⌠41 cosx(0.25x2 + 1.90)dx, use n=3

A: As you didn't mention any question, we will only answer the first parts of these questions. Please…

Q: 3 Estimate e2* sin(x) dx 1 using the Trapezoidal Rule with n = 1,2,4 and 8 segments 2) using Romberg…

A: Part (1): (a)The trapezoidal rule stats that:

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A: Given problem:-

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Q: 1 7. Evaluate the integral -dx using Simpson's method and also find the error comparing ó x +9 with…

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Q: Establish the following integration formulas with the aid of residues: cos x - dx xt + 20x² + 64 `

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Q: 6) Use the successive approximations method to solve the following Volterra integral equation: u (x…

A: The Volterra integral equation is given as u(x)=x22-∫0x(x-t)u(t) dt. We have to solve the equation…

Q: 21) Find the number of compositions M needed so that the error of the integral 2.2 In(x + 2) dx is…

A: Simpson's rule can be used to approximate the value of the integration using numerical integration.…

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Q: By using the reduction formula. integration by parts, one can prove (In (x>)>'dx = x Clncx)^-n…

A: Given formula or integration by parts method: ..............................................(1)

Q: (4) Using Convolution, Solve the Volterra Integral Equation: y(x) = 1 – e-" + y(x – t) sin a dt

A: Given Volterra Integral equation: y(x)=1-e-x+∫0xy(x-t)sinxdt Using convolution it can be written as…

Q: 1. Evaluate the integral 2 1-2 8x cos y dy dr y - 4 by reversing the order of integration.

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Q: 4. Evaluate the definite integral_ TC 3. sin(3t) dt 0.

A: Explained below

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Q: Q1: Verify that the given functions are solutions of the corresponding integral equations by using…

A: Given: ₵(x)=xex and ₵(x)=exsinx+2∫0xcos(x-t)₵(t) dt

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Q: The Particular Integral for the Euler Cauchy Differential Equation d²y dy = x3 is given by x2 + 2y -…

A: Explanation of the solution is given below...

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Q: 6) Use the successive approximations method to solve the following Volterra integral equation: 2 и…

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Q: x² – 25 dx Jx+5

A: Formula: a2-b2= (a+b)(a-b)

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Q: given 3 +3 dz where A J 2x+1 -2x²+X+) and B are integration. 2 and 1 Pespecti vely. Solve the

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Q: Given f (x) = x – z² + 1 %3D - defined over the interval [0, 6]. Use integration methods to solve

A: (a) The interval [1.5, 5] is divided into 8 points, so the 8 points are (1.5, f(1.5), (2, f(2)),…

Q: Find the indefinite integral. (a) / (2* + v#)dx (c) / 2x6 + x5 -dx x4 (4) [(4cs (xỉ + 5x + 4)dx (4…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: 2. す。 sin(x) dE (cosx+1)((05²X +9)

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Q: 1. Show that x = sin (Int) is a solution of t2: (5) 0 = x +1+.

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Q: The Particular Integral of the differential equation (D² – 9)y = 6 cos 3x is PI = 6 sin 3x 18 O PI =…

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Q: by taking n = 2 • dx solution of the integral with Simpson's 1/3 method which one?

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Q: 10. Find the indefinite integral. x – 2 dx x² + 1 -

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Q: Find a formula involving integrals for a particular solution of D.E y" + 3y" – y' – 3 y = tan x

A: In this question, we find the particular solution of the differential equation. Here, we used the…

Q: 1. Evaluate the integral 2 8x cos y dy dx y – 4 by reversing the order of integration.

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Q: Find a formula involving integrals for a particular solution of D.E y" + 3y" – y' – 3y = tan x

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Q: 1. Evaluate the integrals that converge: dx 2x ! dx (x2 + 5)3 b) a) 3-x - 00

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Q: The value of the integral T/2 sin x dx cos(x)e- sin Jo is: Оа. 1-е-1 O a. O b. e- sin 1 O C. С. cos…

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Q: In approximation of 4e* sin(2x) dx by Romberg Integration, R11 = O 2.6842 O 2.9736 O None of these O…

A: Use the following formulae, to estimate the integral ∫abfxdx by the Romberg integration method.…