4.1 Use the trapezoidal rule to find an approximate value for V1+x'dx with n = 4.

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

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Q: 1.4 Calculate an approximate value of the integral S (sinx – Inx + e*) dx by - 0.2 dividing the…

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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: The linear approximation at æ = 0 to sin(2z) is A + Bx where A is:| Previev and where B is: |…

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Q: 2. Use the composite trapezoidal rule with the step length h = 0.1 to evaluate dx I = 1+x2 and…

A: Composite trapezoidal and composite Simpsons 1/3rd rule

Q: `s): The area of the surface obtained by rotating the curve y = ln(3x - 2), for 3 ≤ x ≤ e², about…

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Q: 2. Use Euler's method to find the approximate value of y correct up to 4 dy decimal places for…

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

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Q: Use the trapezoid rule withn=4 to estimate dx . Answer must be in fraction.

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Q: QUESTION 2: Find the approximation for the integral 4 1 S₁ 2x² dx, when applying: the Trapezoidal…

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Q: 4ス+S fra) = 7 +2 Contromulily of he funihim ihe fumnim Discuss The at x= 1

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Q: 12. Find the dicections at.which. the directronal.derivative af.f.(hg)..xSin xy.at.(,a).has.…

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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: Use trapezoidal with 3 level Romberg ( k=3) to evaluate 1 Пх - Пх* cos dx 4

A: The complete solutions are given below

Q: A. Use Simpson's rule to evaluate -dx ,by taking n= 4. Inx B. Find the length of the curve y = x…

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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: B. Use the trapezium rule with 6 ordinates to estimate fe* dx correct to two decimal places.

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Q: Question 8 Set up an integral for the length of the curve yV1+x on 2 sxs3. x2 dx 9(1+x-)5/3 x2…

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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: 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: Use the composite trapezoidal rule with the step length h = 0.1 to evaluate sin x -dx, in six…

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Q: please show all steps

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Q: | 17e dx is accurate to within 0.0001? How large should n be to guarantee that the Simpson's Rule…

A: let f(x)=17ex2 differentiating four times to get fiv(x) because the fourth derivative will be non…

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

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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: A 1125 m³ open-top rectangular tank with a square base x m on a side and y m deep is to be built…

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Q: 2. Find an expression for dy/dx on the curve x In(y) + x³ – 2y = 6.

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

A: The composite Simpson's rule approach is a frequent way to deal with issue. To accomplish this,…

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: In(2x + 2) · dx a) Use Trapezoidal rule with n=4 to approximate the integration b) Estimate the…

A: Given function is ∫04ln2x+2·dx   a) fx=ln2x+2 h=b-an=4-04=1 The function values are  x 0 1 2 3 4…

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: 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: Verify the given linear approximation at a=0 . Thendetermine the values of  x for which the linear…

A: Concept Used: Linear approximation of f(x) at x = a is

Q: Use the trapezoidal rule with n = 4 to approximate S 0.8 0.7 0.6 0.5 1 1.5 2 2.5 3 35 4 4.5 -0.1…

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Q: 3 2 Find for y = dt, where x> 9t+2 dx dx

A: The given function is y=∫0x39t+2dt. Let u=9t+2. Then, du=9 dt. The upper limit will be 9x+2 and the…

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: Show detailed solution to the following using ti integration. x'dx 1. Integration by Parts J Vx4-5

A: Let's find.

Q: Determine the value of ſo1 3.1 X cosx dx by using N= 4 of the trapezoidal rule. Round-off to three…

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Q: The approximation of the integral f(x-1) cos(x+2) dx using two points Gaussian quadrature formula…

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Q: Use the composite trapezoidal and Simpson's rules with step length h = 0.4 to estimate In(2+3/x)…

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Q: 3. Apply Romberg quadrature to •1 1 dx 1+ x2 for h = 1, 1/2, 1/4, 1/8. Show a table of approximate…

A: We are given the following definite integral : ∫1/(1+x2) dx from 0 to 1 And we have to solve it…

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

A: Only one question or maximum 3 parts are allowed . I did 1st integral , for other 1 please repost

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

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Q: 7 1. Approximate dx with six subdivisions to four decimal places using In x A. Midpoint rule B.…

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

A: Kindly go through the explanation

Q: Q2 ) Use the Simpson's rule with (n = 4) to estimate thef²n sinx dx . 2

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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.