1 The approximation of dx by the composite Trapezoidal Rule with n= 2 is +4 O X-

Q: 2. xy dx dy

A: While integrating wrt 'x' we will keep 'y' as constant. While integrating wrt 'y' we will keep 'x'…

Q: ,3 Evaluate the iterated integral dx dy

A: We have to evaluate the iterated integral ∫12∫yy3dx dy.

Q: Evaluate the double integral : 2 e2y+a dy dx

A: In double intregation, first evaluate with dy and then evaluate integral with respect to dx

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: The value of the double integral 7 1 4xy dy dx is 4

A: ∫46(∫274xydy)dxIntregation wrt y so x will be constant.⇒∫46[4xy22]27dx ⇒∫462x(49-4)⇒∫462x(45)dx

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: [2] Determine the values of n and h required to approximate | a In(x)dx to within 10-10. Use (a)…

A: Hello. Since your question has multiple parts, we will solve first question  for you. If you want…

Q: Using an appropriate substitution, 3 the integral S dx equals: /1-4 (х-1)2

A: Here we have to evaluate I=∫31-4(x-1)2dx

Q: 2. Find the value of dx at y=2 if x=z²+5z and z= (y² + 2y)²/3.

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

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Q: Find the solution and the interval of existence for: (1-x2)dy/dx + 2y = (1-x)2

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Q: Evaluate: 1-11-24 = - dx 1 + x 0 By the trapezoidal rule with h = 0.5, 0.25 and 0.125 respectively.

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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: Question The approximation of fxln (x + 5) dx using two points Gaussian quadrature formula is:

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Q: Queston 3.1.1. use the 2xc to approximete dx. Composite Trapezoidal rule with n=4 integral. 3.1.2.…

A: Let us consider y=2xx2-4. We have to compute the approximation of the integral ∫abfxdx, where a=3…

Q: Evaluate xy z? dx dy dz

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Q: 7 xsiny dx + Cx²+1)cosy dy = 0, yC)=TT/2

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Q: Find the general solution: dy = tanxtanydx %3D

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Q: 4 2 1 Evaluate || - dy dx by reversing the order of the integration. O V Y +1

A: Given:∫04∫x21y3+1dydx

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: 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: Find the solution and the interval of existence for  (1-x2)dy/dx +2y = (1-x)2

A: The objective is to find the solution and existence for  1-x2dydx+2y=1-x2dydx+21-x2y=1-x1+x The…

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

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Q: 22. Use the Trapezoidal Rule with n = 4 to approximate 1 (x− 1)² dx

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Q: Use the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+3/x) -dx, 9• I = 1+x²

A: Given: I=∫26 ln(2+3x)1+x2dx

Q: Use the Trapezoidal Rule with n = 6 to ex approximate dx | 1 х Use the Simpson's Rule with n = 6 to…

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Q: 5 一=A+hxsl-x dy=?

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Q: - 3+ In x 3+ In x dy show that dx 2. (i) Given that y = [2] x(3 + In x)? 12 (ii) Hence evaluate dx .…

A: (i) Given : y=-3+ln(x)3+lnx Therefore, taking derivative both sides w.r.t x :…

Q: 3- Approximate xe* dx using h = 0.25. Use a. Composite Trapezoidal rule. b. Composite Simpson's…

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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: 4. Using homogenous D.E approach, solve (x³ – Зху?)dx %3D (у3 — 3x2у)dy. (v³ – 3x²y)dy. | 2 (ardai…

A: The given differential equation is; (x3-3xy2)dx=(y3-3x2y)dy.

Q: Find the integration of (1+ 2x)dx using Trapezoidal and Simpson's Rules for n=6

A: Given integral  ∫061+2xdx The Trapezoidal rule states that…

Q: The value of the integral 1 2 x²y° dy dx is: 2..3 1

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Q: Solve the initial value problem. dy ху?- сosrsinx а. у (0) %3D 2 dx (1- x?)

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Q: Evaluate the double integral dy dx 4. 2.

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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: approximation of I = [" f(x)dx using composite Simpson's rule with n=4 is:

A: In this question, we evaluate the definite integral by using the composite Simpson's rule for n=4.

Q: 10х> — 5х For the integral -dx , if u = x*-x2+6 then Mdu = (10x³-5x)dx, what is %3D x4-x²+6 M?

A: We have integral ∫10x3-5xx4-x2+6dxifu=x4-x2+6

Q: how can i derive this equation in 3 D? *be aqy ay az at Əx

A: Taking heat in three dimensions (I) Net amount of heat conducted into dxdydz per unit time.…

Q: 1. Use residues to evaluate 1 : xe dx , (a>0).

A: Let fz=ze-zz2+a2 The poles of the function fz are ±ai Choose the contour C consisting of the real…

Q: 3) Find dy/dx Cas %3D X-

A: Given:

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

A: Simpson's rules are techniques of numerical integration. Both 1/3 and 3/8 rules are explained in the…

Q: 5) Approximate -dx 1 +: Using the Trapezoidal rule and Simpson's rule with h=1. Find an error in…

A: We have to use both numerical methods for 4 subintervals as h=1 and (b-a)=4.

Q: 37. Use Fubini's Theorem to evaluate dx dy. 1 + xy

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Q: Test for exactness and find the complete solution of dx + [ In 2(x-1) + dy = 0 х-1

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Q: 12) a) Use either the Trapezoid OR Midpoint Rule to estimate [ In(1+e* ) dx using at least four…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.