2 1 The approximation of -dx by the composite Trapezoidal Rule with n=2 is O x+4 0.30833 0.40833 0.40546 None of these 0.20833

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

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Q: 3 Evaluate x² 2 SOFT S S x² sin y dy dz dx

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Q: (1) Use the trapezoidal rule and (2) Simpson's rule, with n= 10, to approxima te the integral. Round…

A: Topic : numerical methods

Q: 10. Evaluate the integral 1 2 S S xe® dx dy ху хе 0 -1

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Q: 2. Given the integral: 4 -dx. Evaluate using Romberg's method. Tolerance = Næ10-6 %3D 1+x²

A: Romberg code: #include <stdio.h>#include <stdlib.h>#include <math.h> double F…

Q: 5) Find the general antiderivatives for the following; х-1 dx x* +2х-3 -dx 6)

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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: 8. Determine the value of n and h required to approximate r2 1 -dx x + 4 to within 10-3 and compute…

A: The value of h and n

Q: 1. Determine the largest possible interval of validity of the solution for the IVP (a2 – 81) + 5ey =…

A: Rewrite the given equation.…

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: 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: 1 7. Evaluate the integral -dx using Simpson's method and also find the error comparing ó x +9 with…

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Q: 2 4 Q3) Evaluate the integral || xe" dy dx 0 x?

A: LetI=∫02∫x24xey2dydxchange the orderI=∫04∫0yxey2dxdyLet∫0yxey2dx=x∫0yey2dx∫0yxey2dx=ey2[x22]0y…

Q: The approximation of 1 = f(x - 1)ex² dx by composite Trapezoidal rule with n = 4 is: 15.4505 -5.1941…

A: Given  I=∫02x-1ex2dx and n=4

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: 2. * S arctan x dx 1 In(x²) + C C 1. x arctan x C A x arctan x -In(x² + 1) + C -- B 1 D x arctan x…

A: Solve the given integration

Q: iSy dx dy 3.

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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: 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: 9-10 Use the Midpoint Rule with n = 4 to approximate the integral. 9. 2² dx

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: I. Find dy/dx of the following: 4. y=√1+In²x 7. y In- COS X √4-3x² 5. y = sin²(In x) 8. y In, x- 6.…

A: Topic - Derivative of a function Power rule: ddxxn=nxn-1ddxln(x)=1x

Q: 2₂/ The ends of the bar X=0 and X= 10 ar kept at temp. o'c and Bo°c respectively. Further the…

A: Introduction: The heat equation is one of the three mos important partial differential equations.…

Q: How large should n be to guarantee that the Simpson's Rule approximation to 19e is accurate to…

A: We need to find how large should n be.

Q: Q8. Using 1/3 Simpson's rule with h = 0.1 estimate (x³ – 3x2 + 2).dx

A: Formula Used: Simpson's 1/3 Rule ∫y dx=h3(y0+yn)+2(y2+y4+ . . . )+4(y1+y3+y5+ . . . )

Q: 2. Find the integral of xe*dx using Simpson's 1/3 Rule with n = 4.

A: Simpson's 1/3 rule for integration :-  here 'h' is difference between each interval which are…

Q: Evaluate the double integral. eln 3 3 7 dx dy In x ey In 3 3 7 dx dy = (Type an exact answer in…

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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: - 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: 18 2 6x dx using n = 2, 4, and 8 subintervals 2

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Q: a) The shaded area is 0• er+2 dx -2

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Q: 1 If y = tanu, u=v--, and v= lnx, dy at x=e? dx what is the value of Select one: a. 0 O b. 1 1 C. d.…

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Q: 1. Using modified trapezoidal, 1/3simpson's rule and 3/8 simpson's rule, find the solution of the…

A: The given problem is to estimate the integral using modified trapezoidal rule, 1/3 Simpsons rule,…

Q: 57 Evaluate the integral |[xy dy dx. 12

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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. 1+x² I =

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Q: Can i get help step by step?

A: We separate the integral into two parts

Q: 27. For what value or values of a does ах |dx 2x x² + 1 converge? Evaluate the corresponding…

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Q: 16 Suppose we know that (3fx)-2)dr-6 4 and that Sxf (x²) dx =8. ise this information and properties…

A: We have to find ∫04fxdx

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

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Q: Using Simpson's method Vx dx for n=4 is equal to

A: We have to evaluate ∫01xdx for n=4.

Q: 2 1. Use Simpson's rule to evaluate | dx , by taking n=4 o V1 + x* 2.Find the Area, enclosed by the…

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Q: 3+ Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx (3e)3+ sinh2x A +C 2+In3 (3e)3 + cosh2x +C…

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Q: Q1 Evaluate the following: Ine dx n/3 4 sinx 1- Jo 2- Jo x(Inx)2 3-m 2e*cose*dx in 1-4cosx

A: Simple integration problem.....

Q: 1+x Find the approximation of dx using Simpson's rule with step size h = 1+x2 0.25.

A: Simpson's rule: numarical methods

Q: Q2// 1.5 I= S dx use Simpson's 1/3 rules, with n=4. 0.2

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Q: 1 Using Simpson's method | Vx dx for n=4 is equal to Blank 1 (use 2 decimal places with proper…

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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.