Approximate 4 1 dx 1+ x Using the Trapezoidal rule and Simpson's rule with h=1. Find an error in each case.

Q: x² dx %3D Use right endpoints and = 10 rectangles to find an approximation of

A: Given, Use the endpoints and n= 10 rectangles

Q: The following problem is for extra practice and does not have to be submitted. 2 1 -dx using the…

A: According to question ∫0211+x3dx,       n=4

Q: If x° + y = 65, find the value of at the point (4,1). dx? dy at the point (4,1) is- 2 dx The value…

A: x3+y3=65 Differentiating with respect to x, we get 3x2+3y2·dydx=0    ∵dxndx=nxn-1  &  dcdx=0,…

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A: According to Gaussian quadrature with 2 steps, ∫abfxdx≈c1fx1+c2fx2 Where…

Q: 4 dx. x'V16-x (c) By using x= 4sin (0), find

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Q: (a) By using the substitution, u = 1 + x*, or otherwise, find x3 -dx 1+ x4

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Q: The value of 'n' to approximate [x dx by taking h = 0.1 using Trapezoidal Rule is О а.2 O b. 5 О с.…

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Q: 3 Given that 3. e dx = e° - e, use this result to evaluate 3ex + 4 dx.

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Q: find dy/dx in terms of x and y if (x-a)^4+y^4=a^4. Assume "a" is a constant dy/dx=?

A: Given: (x-a)^4+y^4=a^4

Q: 4-S cosh? Vx dx x csch vx

A:

Q: 4. Find an approximate value for fo In 1+x³| dx.

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

Q: dy Find by differentiating implicitly. When applicable, express the result in terms of x and y dx…

A: As per guidelines we can answer only the first question, so if you need more answers kindly repost…

Q: Using the Trapezoidal Rule, an approximate value of 5 V(x + 3x)dx with 5 ordinates, correct to one…

A: Consider the given integral.

Q: (b) Find the value of e dx taking n = 6, correct to 5 significant figures by Simpson's one-third…

A: Find the value of ∫00.6 ex dx taking n =6 ,correct to 5 significant figures by Simpson's one-third…

Q: The approximation of I = (x-3)e* dx by composite Trapezoidal rule with %3D n=4 is:

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Q: 4 dx 1+ By using (Answer one only) a- Trapezoidal rule when n=5 b- Simpson's rule when n=6

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Q: Find dy/dx by differentiating implicitly. When applicable, express the result in terms of x and y.…

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Q: Use the trapezium rule, with 4 strips, to estimate ? e−x2 dx on [0, 2]. What is the maximum error?…

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Q: Q1/ Answer the following: 1- " |x | dx = ? 2- ofw4 sec² x dx =1

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Q: 1. Use a substitution to find (6x2 2)e*+¤ dx showing working.

A:

Q: Find dy/dx for the Following!- secx 13x Cot 5x (2In 9x)

A: Find dydx of the following:y=lnx4secxtan-1e3x6cot5xe2ln9x

Q: 42. (a) By completing the square, show that 1/2 dx T x² – x + 1 3/3

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Q: cosh(lnx)dx 4. f 5. [* cosh vxdx 6. Jo Sm 10 4sinh? () cosh ) dx

A: Solve the three questions.

Q: Suppore velue fx) = x". Find Hhe valhe %3D fli.0) using finst-or for appresimaton

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Q: 33.) Show all steps to evaluate by hand: 4-х2 Vx2 + y2 dy dx

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Q: 0.8 Evaluate e* dx using-trapezoidal rule by breaking it into 5 intervals. 0.3

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Q: Use the Errors in the Trapezoidal Rule and Simpson's Rule cos(4nx) dx

A:

Q: (a) Use n = 6 subdivisions to approximate the value of 6 Vx + 3 dx by the trapezoidal rule.

A: We need to find approximate value by trapezoidal rule. NOTE - AS PER OURGUIDELINES WE CAN NOT SOLVE…

Q: Find the value of b so that (2x – 1)dx = 10 - 1 3 O 2

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Q: While evaluating the approximate value of x2 dx, using Trapezoidal rule, taking h = 0.5, 3 the value…

A: Given integral: ∫36x2dx h=0.5 To find: the value of N=?? [no.of sub-intervals]

Q: 6. Find values for A and B so that Let y %3D +10 dy dx where %D A = B =

A:

Q: Use n = 6 subdivisions to approximate the value of Vx +2 dx by the trapezoidal rule.

A: The given integral is ∫06x+2dx and the value of n is 6. Using the trapezoidal rule, approximate the…

Q: How would I do this question?

A:

Q: /2 dx by completingquam, show thad 353 スーx+

A: The integral function is ∫012dxx2-x+1=π33.

Q: 1 dx using the trapezoid rule with n=4 1+x d. Use your answers for parts a and b to estimate

A: Given the integration ∫0211+x3dx

Q: dx 7. S; x³ Vx2-4

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Q: Find 3 for 2 = In (xº dx Provide your answer below: +y¹).

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Q: 56 Given that: S V56x - x² dx Find the value of m

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Q: - y = V1 – sinx

A: Given,y=1-sinx3y=1-sin(x)13Differentiate w.r.t. x using chain…

Q: 2- Evaluate sin x dx using i. Trapezoidal rule ii. Simpson's rule iii. Simpson's rule, taking n = 6

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Q: Find appropiate in tegrating and solve the equation an 3 323? dx + こ

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Q: dy Find for x=secy dx A xsinx B D 1-x?

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Q: (a) Evaluate by solving the work for (i) Sxe-*dx.

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Q: 0.2+ 25x+ 3x2) dx

A: Simpson's 13 rule: ∫abdx=h3(y0+4(y1+y3+y5+...++yn-1)+2(y2+y4+y6+...+yn-2)+yn)   Simpson's 38 rule:…

Q: Find an upper bound for the error in estimating (5x3 + 2x)dx using the Trapezoidal Rule with n = 10…

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Q: 1 dr rVx* – 4 #8.

A: The given integral is ∫1xx4-4dx. Let u=x4-4. Then, du=4x3 dx. Apply the substitutions and evaluate…

Q: 2. dx tanx 4t² dt

A: To differentiate the given function.

Q: (a) Use n = 6 subdivisions to approximate the value of Vx + 3 dx by the trapezoidal rule.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 2х dx e2x

A: We have to solve the integral

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.

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.