4, and f(2/5) = f(4/5) = c. Suppose that the approximation of I = f; f(x)dx by composite Trapezoidal rule with 5 subintervals is 1.8, then the value of c is: 0.5 4 O -0.5 O 2

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Q: The integral of the given function ſ 3(x-1) dx is equal to (3x+1)ž

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Q: (2.5 + 3.8x? – 1.6x³ + 14.2x5 – 8.1x)dx

A: To Evaluate the following integral: I=∫13(2.5+3.8x2-1.6x3+14.2x5-8.1x6)dx a) analytically; (b)…

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: Solve the following boundary value problem with the Galerkin method in which two equal length…

A: In the Galerkins method of approximation the trial function itself is considered as the…

Q: a) If | f (x) de f(x) dx = 2, find 1 (3f(a) – 1) de. = 7 and || - /4 (b) Estimate the value of the…

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Q: Q5. Find the below integrals and √(2.20) 2717 dx(x) = 2₁ (0,00) 1 + X{0,3} + X(-3,-2)) "dX=? where A…

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Q: 1. Approximately compute the value of the following integral, as accurately as possible, using the…

A: Note:- Here, you mention function f(x) is creating little bit confusion for me. Is…

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

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Q: Q8. Using 1/3 Simpson's rule with h = 0.1 estimate (x - 3x2 + 2). dx

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Q: Given the initial conditions y(1)=1 and y'(1)=0, estimate y at x=1.2 using a stepsize h=0.1. Use…

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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: The integral J dx reduces to e+1 where u = f(x) and for some constant k.Compute f(1).

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Q: We would like to solve the following boundary value problem using the weighted residual method: d'u…

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Q: (b) Evaluate 1 dx using Romberg's S. 1 + x2 hence obtain an approximate value of T.

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Q: 2xydx+(x2-y)dy=0

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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,…

A: The secant method is used to calculate the root of the function. The formula for the secant method…

Q: (a) Consider the task of approximating e-4=* dx using the Composite Trapezoidal rule. How large…

A: As per bartleby guidelines we only give first question answers.

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…

A: Estimation of minimum number of intervals

Q: Q3) Approximate the integral e* cos x dx using the composite Trapezoidal rule with M=5 subintervals.

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Q: In the given DE, cos z + In y + ( +e) dy 0, de integrating M (x, y) with respect to x generates a…

A: Here we are given a differential equation And we have to find the function g(y). For this first we…

Q: We would like to solve the following boundary value problem using the weighted residual method: d'u…

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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: 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.…

Q: (ylny - e¯xy)dx + ( + x lny) dy = 0

A: The differential equation Mdx+Ndy=0 is said to be exact differential equation. If it satisfies the…

Q: The integrating factor of the given DE are already given below. What is the value of "n"…

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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: The approximation of x' e¯*dx by Simpson's Rule is O 0.162402 O 0.160603 O 0.160602 O None of these…

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Q: Q1: Use Newton - Raphson method to estimate the 3 Voot of fcx) = x -X - 1, e mp loying an initial…

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Q: The correct value of dx is equal to 3-x O A. Since the integral converges to 2/3, none of the given…

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Q: Given: S^(1+ 2x)e-* dx. Using integration by parts and letting u = -1- 2x, dv =¿f(x)dx, then the…

A: we have to evaluate, ∫0∞1+2xe-xdx Let u=-1-2x and dv=32-23e-x where fx=-23e-x…

Q: We would like to solve the following boundary value problem using the weighted residual method: d'u…

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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: 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: For a. y′ =ln(y)+x,withy(1)=1. (Here x0 =1.) b. y′ =ln(1+y),withy(1)=0. (Here x0 =1.) Is it…

A: Solving for  a) y'=ln(y)+x            dydx=ln(y)+xdy=ln(y) dx+x dx Integrating:           ∫dy=∫ln(y)…

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

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Q: Si (e0.5x +sin2x)dx, use n = 4

A: Solution

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: Given: 6°(1+ 2x) e¯* dx. Using integration by parts and letting u = -1– 2x, dv = ÷f(x)dx, then the…

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Q: The value of the triple integral (x² + y²)dV where E is the E portion of x² + y² + z² = 4 with 0 ≤ y…

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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: To evaluate the integral * dx we use the substitution e а. x2 1 O b. 1- x2 O d. x + 1 =t

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

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: 5. Given the function f(x) = 1 + ex sin(4x) with integration limits from a = 0 to b = 1. Use…

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Q: By the even extension method applied to the function f (x) = e-2", where x > 0, the value of the…

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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:…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.