8. Determine the value of n and h required to approximate r2 1 -dx x + 4 to within 10-3 and compute the approximation for n = 4. Use the Compo Trapezoidal rule: п-1 h b – a | f(r)dr = lf(a) + f(b) + 2 £ f(x;)] 2?f"(µ) 12 j=1 with h = (b – a)/n.

Q: Q3) Solve the following boundary value problem using finite difference method dy +2y = 0 dx y(3)=…

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Q: ölüm 5/ 11 - - Soru 5/11 Evaluate the following integral dx. (x² + 9)(x + 2) (Maksimum karakter…

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Q: Estimate the error in using the Trapezoidal Rule with n=8 when approximating the inetegral of…

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Q: 3 3 4 Evaluate the integral S [(?+y?+?)dz dy dx. 0 0 0 3 3 4 S[?÷+²)dz dy dx=O 0 0 0 (Type a…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Suppose f(0.25)=f(0.75)=b. If the Composite Trapezoidal rule with n=2 gives the value 4 for \int_0^1…

A: Introduction: The trapezoidal rule is a method to approximate a definite integral numerically. In…

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

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Q: 2. Integrate numerically the given function, fx0.1(1.2-x)(1-e20(x-1)) dx with the multiple-segment…

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Q: Determine the approximate integration of the following using simple & modified trapezoidal,1/3…

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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: Let dy/dx =f(x, y)= x^2 -y Use Euler’s method ( with step size ℎ = 1) to approximate the value of…

A: Given, dydx=f(x,y)=x2-y y(0)=1 h=1

Q: e the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+3/x) dx. -dx, 1+x²

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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: Jse the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+3/x) 1, dx, 1+x2 I =

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Q: The approximation of - 1 dx by the composite Trapezoidal Rule with n= 2 is x+4 O 0.40833 O 0.40546 O…

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Q: Use Secant method to to approximate the solution of f(r) = z+ cos z =0 accurate to within 10-3,…

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Q: Express the general solution of dy/dx = 1+ 2xy in terms of the error function erf(4) = dt.

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Q: 47) Estimate the minimum number of subintervals needed to approximate the integral 2 S (7x4 - 1x)dx…

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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: 36. Using the approximation dy dy h dr * Yn+1- y. and that dr 1, y = 2 when r 0. Then, y A h- 2 h+ 2…

A: Please see the answer below.

Q: · Use fourth-order Runge-Kutta Method to solve the following problem over the interval from x 0 to…

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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: 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: (a) Compute the average temperature of a wire in the shape of a helix c(t) = (cos(t), to, sin(t)), t…

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Q: 2 1 The approximation of -dx by the composite Trapezoidal Rule with n=2 is O x+4 0.30833 0.40833…

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

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Q: 9. a) Apply fourth order Runge-Kutta method to dy 3x + y/2, y(0) = 1 dx to determine y(0.2) correct…

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Q: How large should n be to guarantee that the Trapezoidal Rule approximation to 8 | (- 2* + 20z – 96z?…

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Q: Compute an approximation to the value of Le-x*dx a) using Simpson's Rule b) using Simpson's…

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Q: Use fourth-order Runge-Kutta Method to solve the following problem over the interval from x = 0 to…

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Q: 2) Evaluate the following integral: L(a - x- 4x³ + 2x*) dx (a) analytically (b) single application…

A: Given Integral: ∫-24(1-x-4x3+2x5)dx

Q: Use the composite Simpson's 1/3 rule with step length h = 0.4 to %3D estimate I = [ S" In(2 +3/ã)…

A: Given that, the integral is ∫26ln2+3x1+x2dx and step length is h=0.4=25. From the given 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: Find a positive value of k for which y=sin⁡(kt) satisfies d2y/dt2+16y=0.   k=

A: Double derivative

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A: See the attachment

Q: (a) Find the differential dy. V3 + x2 dy = (22+3)() (b) Evaluate dy for the given values of x and…

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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…

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Q: Evaluate the line integral / (2x + 7y)dx + (4x – 6y)dy along the curve C: = 6 cos t, y = 12 sin t…

A: Let's find.

Q: · Use Euler's Method to solve the following problem over the interval from x = 0 to 1.0 using a step…

A: Given, f'x,y=dydx=2+3xyy0=1 Euler's method is given by, yn=yn-1+hfxn-1,yn-1

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: Q.1) Evaluate the following integral ez dx (2e2 – 4e* – 1) - -

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Q: Use the Runge-Kutta 4th order method to solve 10(dy/dx) = x2 + y2, y(0) = 1, for the interval of…

A: Given y′=(x2+y2)/10 , y(0)=1, h=0.1 Forth order R-K…

Q: Determine the approximate integration of the following using simple & modified trapezoidal,1/3…

A: Kindly go through the explanation

Q: use euler's numerical method to obtain an approximation of y (0.6) with h = 0.1 where y(0.2)=1

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Q: Q1/ Evaluate 1 dx Jo 1+x² using Simpson's 1/3 rule Simpson's 3/8 rule i- ii-

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Q: Use the Error Bound to find the least possible value of N for which Error (SN) <1 x 10 9 in…

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Q: -4 I cosx (0.25x² + 1.90)dx,use n =3

A: Given:        ∫14cosx0.25x2+1.90dx , n=3 The formula for the Trapezoidal rule:…