(b) Consider the integral I = So f(x)dx for the function 1 f(x) = -2e-* + 4 2x 120 Approximate I using the Composite trapezoidal rule with N = 4.

Q: (b) Find a value for n to ensure that the absolute error in approximating the integral xsin x dx by…

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Q: Suppose f has absolute minimum value  m and absolutemaximum value M . Between what two values must…

A: Given that the absolute minimum value of f(x) is  m and absolute maximum value is M So,…

Q: Q5. Approximate the integral | Sin(2x)dx (i) Using composite Sympson's rule with n = 2,4 and Romberg…

A: Given the integral ∫-11sin (2x)dx.

Q: Find x" In x dx; n # -1, n real. (Use C for the constant of integration.)

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Q: 1. Use the midpoint rule with n = 6 to estimate the value of the integral (x3 + x)dx.

A: We need to estimate integral value. NOTE - As per Bartleby's guidelines we can solve only one…

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: 4. (a) (b) Approximate the integral f x² cos xdx with n = 6 using the composite trapezoid rule;…

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Q: Evaluate the integral. (Use C for the constant of integration.) √x²√3 dx √3+2x-x²

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Q: Evaluate the integral. (Use C for the constant of integration.) x² + 9x + 1 dx (x² + 1)2

A: Make two parts of the integration.

Q: 1. Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x) dx.

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Q: 2. Find the interval [a, b] for which the value of the integral (2 + x − x²) dx is a maximum.

A: ∫ab(2 + x -x2 )dx here for get maximum value we have to differentiate the function  so here first…

Q: Evaluate the integral. (Use C for the constant of integration.) x2 + 7x + 1 dx (x2 + 1)2

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Q: Use the tabular method to find the integral. x²(x – 2)/2 dx

A: Use tabular method to find the integral  ∫x^2(x-2)12dx sign Derivative Antiderivative + x2…

Q: Queston} $²3 20c x²-4 Composite Trapezoidal rule with n=4 dx. 3.1.1. use the to approximate…

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Q: Find the length of the arc of x2 + y2 = 64 from x = -1 to x = -3, in the second quadrant. (Solve…

A: We need to find arc length.

Q: Solve the ODE: dy (x' +4x) 0 using separable variable method: dx x(sin 2y +4)

A: The differential equation is as follows : dydx-(x5+4x)x(sin2y+4) = 0 Hence we get dydx =…

Q: Evaluate the double integral 1 2x+1 LL.** Select one: | None of them 113 x² dy dx

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Q: a) For 0 ≤ x ≤ 1, show that < x². √2 + x b) Use the estimate in a) and integrate it to prove that…

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Q: 18x? Evaluate the integral: -dx V49 – x2 -

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Q: Use the bise ction to approximate the solution of F(X)=Vx - cos X = 0 accurate to within 10 -3 on…

A: Bisection method: In order to find root of equation f(x)=0 in a,b such that f(a)f(b)&lt;0 Bisect the…

Q: Evaluate the integral (2a+4)(x² + 4x + 2)*dx 4 by making the substitution u = x+ 4x + 2. ,2

A: Let u=x2+4x+2, now differentiate it with respect to x. du = (2x+4)dx So,…

Q: Use integration by parts to prove the reduction formula: п-1 S (In x)"dx = x(ln x)" – n [ (Inx)"-! п

A: 2

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: Consider , xe¬**dx. What will be the appropriate solution and answer to this improper integral? A.…

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Q: 79. What are the new limits of integration if we apply the substitution u = 3x +7 to the integral…

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Q: 4. Use the definition of integration to find (1+2x' ) dx , that is find lim f(x; )Ax

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Q: Calculate the approximate to the integral -5 (24 +2x² − 3)dx, by the composite midpoint rule with…

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Q: 8. Find the value of the constant C for which the integral 11x 11C dx x* + 1 4x + 1 converges. C =…

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Q: 5. Find the indefinite integral. A) f dx (x-3)Vx -6x+5

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Q: Use integration by parts to establish the reduction formula: Jx" cos x dx = x" sin x – n x*-1sin x…

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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: 1. Use integration by parts to prove the reduction formula S(Inx)" dx = x(lnx)" – n S(Inx)"-1dx. %3D

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Q: O f(3x² + sec² 2x) dx

A: Given query is to find integral.

Q: Compute x² In a dx both analytically and numerically. Use trapezoidal, Simpson's 1/3, Simpson's 3/8…

A: For the solution follow the next steps.

Q: 2. Use the error formula to estimate the error in approximating the integral T/2 2 sin x dx using…

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Q: Q3/ Find the integral x e* dx by using trapezoidal and simpson methods with an error of no more that…

A: According to question given :Integral ∫01x ex dx by using trapezoidal and simpson 38 methods with An…

Q: 2. Use integration by parts to establish the reduction formula: Sx" cos x dx = x" sin x – n x"-1 sin…

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Q: Evaluate the integral. (Use C for the constant of integration.) x² - 36 dx v3

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Q: 3.a) Apply the Trapezoid and corrected trapezoid rule, with h =, to approximate the integral £mcx+…

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Q: Find the minimum value of n that guarantees an error of no more than 1/30,000 in approximating the…

A: Given the integral: Hence we have

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: (b) Approximate the definite integral f"/² cos(x)dx by employing the Composed Midpoint rule with n =…

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Q: Sx". .n-1 + n[x²- x" sin x dx = -x cos x + n cos x dx

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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 S sin (ax)cos(ax)dx

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Q: Evaluate the Double Integral. 4 V16-x2 b. 2x dy dx

A: We have to evaluate

Q: Q5. Approximate the integral Sin(2x)dx (i) Using composite Sympson's rule with n = 2,4 and

A: As per the policy of bartleby the provisions is to solve only one question at a time so I am solving…

Q: Use multiple application of the trapezoidal rule to numerically integrate : f(x) = = 400 x ² - 900…

A: It is a Numerical Analysis problem. Let us estimate the value of the integral numerically using…

Q: 1. Use the midpoint rule with n = 6 to estimate the value of the integral x³ + x)dx.

A: