By the even extension method applied to the function f (x) = e¬16x, where x > 0, the value of the integral cos(1w) = e-1ox, where dw = 256 + w2 IT 1. el6 - 16 1 2. el 32 3. ле-1 IT 4. e 16 32

Q: That the value of the integration g(1) = 00 , g(2) = 0 1-e t) -dt 9(t) where g is a function that is…

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Q: Evaluate the integral: e³+cosh2x33+cosh2xsinh2x dx A (3e)3+ sinh2x 2In3 + C (3e)3+ sinh2x B 2 + In3…

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Q: 2. Consider the functions: f(t)=√1+t² and g(t) = 2t Find the convolution of the two functions by…

A: We have to find convulation of given function.

Q: According to numerical methods, the integral of a function f(x) over the limits a and b can be…

A: Given data  Used Simpsons 1/3 rule  f(x)=7e^(-πx)(sin(x^2)) With a=0 and b=2 and number of intervals…

Q: Q3. (30pt) Calculate the integral 2x³ – 4x + 1 - (1– cos x) dx 1+x? a) for n= 10 according Simpson…

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Q: 2. Suppose | 29(r)dr = 10. Using linearity properties of integrals, calculate | (g(x) + 3)dx. 3

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Q: b. Find the value of V1- 0.162sin²x dx using Simpson's 1/3rd rule, taking 6 equal subintervals

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Q: Evaluate the integral: Se3+ cosh2x33+ cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 - + C (3e)3 + cosh2x B…

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Q: 2.) Evalvate the Integral ودل أاد-ل (x² _33² dx, .3 2 by making w - x²-3 NOTE: Answer should be in…

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Q: The area between the curve X= t2 - 2t+1, y= In(t) and the y-axis for 1sts5 would be found by setting…

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Q: 1. If f(x) dx = 3, evaluate [[1 + 21(x)] dx using the properties of interga 2. If f(x) dx = -2 and…

A: As asked we can answer question no 1 and 4 as below.

Q: Determine whether each of the following integrals is proper, improper and convergent, or improper…

A: We need to determine  whether each of the following integrals is proper, improper and convergent, or…

Q: Use the modified Euler Method to solve the ODE = subject to y 1 when x 0 %3D dx 1+x on the interval…

A: To find y(0.3) by using the modified Euler's method.

Q: Q1 (a) Integrate the following definite integrals using suitable method: (i) S, tan-1 x dx (ii) a dx…

A: To evaluate the given integral

Q: By the even extension method applied to the function f (x) = e¬19x, where x > 0, the value of the…

A: Given, fx=e-19x where x>0 using even expansion Let fevenx=e19x      -∞≤x<0e-19x        0≤x≤∞…

Q: Q4) A) Find by using chain rule if f = ( , u=-1, x=-1 dx ++1 B) Evaluate the following integral: V2…

A: Given f(u)=u-1u+12   , u=1x2-1    , x=-1

Q: Choose the most appropriate answer: Evaluate the integral : J(e- 182 + sin 11x) dx -18x e + cosll +C…

A: We need to evaluate the following integral : ∫e-18x + sin11xdx

Q: 90% of it Suppose dy/dx = x-y and y = 2 when x 1, Use Euler's Method with increments of Ar = -0.1…

A: Given the differential      dydx=x-y with y(1)=2. Find y(0) using Euler's method with step size…

Q: (4)Evaluate the definite integral (a)S(1 + sin x )£x 1/2 (b) [ (2t + cost)dt -*/2 x +1

A: As per the Guidelines, I will answer the first 3 Integrals. For the fourth one please repost the…

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: From the differential equati on by eliminating the arbitrary function ffrom xyz = f (x?+y'+z°).

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Q: If 9. 3. 6. f(x)dx = || f(x)dz + 6. what are the bounds of integration for the first integral?…

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Q: Q2:- Apply romberg's method to the integral of f(x) = nx*cos(-Tx to 2 with Tol = 10-4

A: Given function is f(x)=14πx4cos14πx, we have to integrate above function from 0 to 2. Formula for…

Q: Q1 (a) Evaluate the integration of the following functions: (iii) | (3x3 – 2x 2+1)sinh 2x dx by…

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Q: Solve the Indefinite Integral. xe²t S dx (2x+1)² A [1-21] +0 e2x 2x C 4 2x+1 B. 2-2(22+1) + C 4 C.…

A: SOLUTION-

Q: The integral of the given function | sin 9x cos 4x dx is equal. .... 13 cos(5x) — 5 сos(13x) А. + C…

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Q: 4. Use residues to evaluate the improper integral 1t r4 a + x2 dx; where a is a real constant.

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Q: Evaluate the following indefinite integrals. 1. S(5x + 4)11 dx 2. Sx (x² + 2)17 dx 3. fx²(9 – x³)5…

A: The solution is given below

Q: y" +Zy+3y=sin (3x)

A: Given that,  y''+2y'+3y=sin(3x) The auxiliary equation is m2+2m+3=0m=-2±4-122=-2±2i22=-1±i2…

Q: Consider the IVP: x" + (x')² +5tx = 0, x(0) = 2, x'(0) = 3 Using the Euler method with a time step…

A: We apply the Euler's method to find the solution we apply the transformation U'=V and V'=-V^2_5tU,…

Q: Find the antiderivative for the given function. 3x tanh(x*) 1) In(cosh(x*)) +C 2) In(cosh(x*)) + C…

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Q: Step by step

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Q: x² – 25 dx Jx+5

A: Formula: a2-b2= (a+b)(a-b)

Q: Find the value of the improper integral or state that it is divergent. (If it is divergent, enter…

A: We will calculate the definite integral using basic definite integral properties and if we get an…

Q: Find a bound for the error in the approximation T20 to the given integral (but do not calculate…

A: Find a bound for the error in the approximation T20 to the given integral∫0217e-x8dxEnter the error…

Q: tanh (22) d) evalvare J seen 2 (2n ) e レッ using a substitution Suitable

A: To evaluate the given integral.

Q: What is f'(x) given the integral function •5x+1 f(x) = 5x+¹ cos(e") du? ○ f'(x) = 5 cos (es) o f'(x)…

A: We have to find out derivative

Q: (c) Determine the arbitrary constant of integration for the integral: y = [(4t -5-dt given that y =…

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Q: b. Find the value of V1-0.162sin²x dx using Simpson's 1/3rd rule, taking 6 equal subintervals

A: We apply Simpson 1/3rd rule it is given that six sub intervals must be mentioned so in the interval…

Q: se N.P.M. to estimate the root of -X = e -X for an initial of Xo =0

A: Here f(x)=e-x-x,  x0=0. We estimate the root of f(x)=0 by using N.R.M.

Q: If | h(2)dz = 4 and | h(2)dz = 9.1 %3| 1 what does the following integral equal? |h(2)dz = 4

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Q: Q4: To evaluate the integral fcos' xdx using the reduction formula of cosinc function

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Q: 2. Evaluate the improper integral S₂ (5. dx (5-x)4/3 or state that it diverges.

A: The given integral,      ∫28dx5-x43

Q: integral of C(1-e^(-bt)) with the initial time being 0

A: Let's find.

Q: 1 and use it to estimate In(1.26). Find the linear approximation of f(x) = ln x at x L(x) = In(1.26)…

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Q: 1. What should be A for the path independent of (2,4) xy + A dx + 2Ay – x y? fip- (1,2) Moreover…

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Q: s the indefinite integral | x2 cos(x3) dx becomes 1 cos(u) du- must also convert the integral…

A: Given query is to find the integral limits.

Q: 2. Evaluate the following Integral by using suitable method: 2y3 + y y4 + y2 + 1 dy -

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Q: In item number 5, the integral of Sx3 dx is obtained by applying what Basic Theorem of…

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