Q5. Approximate the integral | Sin(2x)dx (i) Using composite Sympson's rule with n = 2,4 and Romberg integration. (ii) Using Gaussian quadrature with n = 3

Q: Q-4) Find the integration of function (f (x) = x2 + 1) by using "Simpson Rule" when (n=6) on the…

A: Simpson's rule is used to approximate the definite integral which represents the area under the…

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Q: Use contour integration to compute the following integrals. (a) 1. 2π cos(20) dv 5+4 cos v

A: (a) Given integral ∫02πcos(2ϑ)dϑ5+4cosϑ. The objective is to compute the integral by using contour…

Q: Q3: Answer Only ONE question, either (A) or (B): (A) Evaluate the following integrals 1. 1=jx sin'x'…

A: Q-3As per bartleby guidelines we only give first three subparts questio answerA1  I=∫x sin3x2dx…

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:

Q: Evaluate the integral I= [²₁x² + cos compare with exact solution. dx using two point and three-point…

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Q: Equation: Answer:

A: We want to find value of x. For this we use Pythagoras theorem, which states that Hypotenuse2 =…

Q: A scientist uses the one-point Gauss quadrature rule based on getting exact results of integration…

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Q: 2. Consider the problem of evaluating the value of the definite integral 2х-п dx . sin(x) i) Apply…

A: According to the Given question; I=∫022x-πsinxdx Ans 1; By Monto Carlo Method; I=∫022x-πsinxdx…

Q: 3) Evaluate the following integrals i). /²(6+3 cos x) dx ii). (1-e-²x) dx iii). ₂(1-x-4x³ + 2x5) dx…

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Q: Estimate the minimum number of subintervals needed to approximate the integral dx with an error of…

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: Which method approximates (x³ + Inx) dx to 0.9314 (a) trapezoidal rule with 12 intervals (b)…

A: Trapezoidal rule ∫x0x0+nhfxdx=h2y0+yn+2y1+y2+y3+y4+...yn-1 Simpson's one-third rule…

Q: 3 (х3 — Зх2 + 4х — 5) dx | a) Approximate the definite integral with the Trapezoid Rule and n = 4.…

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Q: 8 dx QI Evaluate | by trigonometric substitution integration method? (1+x)

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Q: Find f(t) given that f"(t) = 6t + cost, f'(n) = 2 and f(0) = 3. Do not simplify the second constant…

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Q: (13) Evaluate the integrals: (a) o sin¹ (30)d0. z+4 (b) Sdz. (c) Sdt. ၂ 3 2 x-4

A: We have to evaluate the following integrals: (a) ∫0πsin43θ dθ. (b) ∫z4z+4dz. (c) ∫23xx-4dx.

Q: (b) Solve the integral [(3x– y)dx+(2x+3y)dy along the curve x = y³ from (0,0) to (1, 1).

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Q: Q3: Reduce the integral Sx³J2(x) dx to integration in terms of Jo(x)

A: To find - Reduce the integral ∫x3J2x dx to integration in terms of J0x.       Formula used - Bessel…

Q: Q1: Evaluate the following Integration: a) ( In(x²+x)-Inx-en3 dx b) S; sinx Ine(x+1) 1-cos²x

A: Answer (a): To evaluate this integral, apply the logarithmic properties : And, And, And, And,…

Q: 8.(5.4) Change the order of integration and evaluate. (1) I = √² S 1 1 cos(x + y) dy dx (2) I =…

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Q: -16 dx 1. X=2 sec(e) 2. x= 2sin(e) 4-X dx 3. X= 4tan(e) 4. X= 4sec(e) SV16+ x² dx x²-4 dx

A: See the details solution in below

Q: Q/5 Evaluate the integral of: (a) St³et* dt dx (b) 2 x (In x)²

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Q: (a) / 3x2 + 5x + 8 dx (x2 + 1)(x + 2) (b) / 2V1– x*dx .5 - (e) J, T- dx 1+ e*

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Q: 10) evaluate the integral (Usec for theconstant integration e- cos (ro)de

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Q: Q4: Evaluate each of the following integrals: (a) | (4+ cos x)· sin x dx (Substitution)

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