Q4 Consider the integral dx . (a) For which value of n the error in trapezoidal rule will be less than 1.2x10 (b) For which value of n the error in Simpson's rule will be less than 2.5x10*. (c) For the value of n obtained in parts (a) and (b) compare the error and the error bound.

Q: Use Simpson’s Rule with n = 4 to approximate ∫1  ex^2dx

A: The given function is continuous on the interval [0, 1], then using Simpson’s rule to find the…

Q: (b) Find a value for n to ensure that the absolute error in approximating the integral xsin x dx by…

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Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral S7 n = 20…

A: we nee to find ∫π4π2ln(tanx)dx,  n=20 a=π4=0.7854,  b=π2=1.5708 ,  y=ln(tanx)…

Q: Consider the integral -6e-l dx If the integral is divergent, type an upper-case "D". Otherwise,…

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Q: Q5. Approximate the integral | Sin(2x)dx (i) Using composite Sympson's rule with n = 2,4 and Romberg…

A: Given the integral ∫-11sin (2x)dx.

Q: •3 Evaluate the integral / | 0. dx dy by reversing the order of integration. NOTE: Enter the exact…

A: This question is related to double integral, We will solve it using given information.

Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral   [ 2x 3  - 3…

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Q: Evaluate the integral ,(1 – x – 4x³ + 2x³) dx a) Analytically b) Single application of trapezoidal…

A: we have  f(x)=1-x-4x3+2x5 we need to find ∫-24f(x)dx  a) analytically b) using trapezoidal rule

Q: Using residues, calculate the improper integral 1 dx . 1+ x4

A: By using residue theorem the above integral is solved as follows

Q: Q3. Use tabular integration by parts to evaluate the following Integral (x² +x+ 1) sin x dx

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Q: a) For what value of a is the integralf dx improper? Explain. x+2 b) Does this improper integral…

A: we have

Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral In(tan x)…

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Q: Using reciprocal substitution x=-, the integral -dx reduces to (z- 1) 1/3 © -/t- dz 1/3 © - /(?-1)…

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Q: b What value of a and b that minimize the integral : (x* – 2x²) dx a (Hint: Where is the integrand…

A: We have to find the value of a and b

Q: use integration by parts to establish the reductionformula.

A: Integration by part formula: ∫uvdx=u∫vdx-∫u'∫vdxdx

Q: The integral dx is improper for two reasons: The interval [0, co) is infinite and the integrand has…

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Q: 4) Use the Midpoint Rule to approximate the integral. Then evaluate the actual integral. L(3x - 7)²…

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Q: Q2 Approximate this integral using Simpson's rule whose abscissa and weights are given by {-1,0,1}…

A: Please check step 2 for the solution

Q: Estimate the integral below by using Simpson's rule and Trapezoidal method with n=4, also find ET…

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Q: Consider the integral Í dx . For which value of n the error in trapezoidal rule will be less than…

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Q: 3. Does the improper integral 2 dx converge? et +e-*

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Q: Use Simpson's Rule with n = 4 to estimate the following definite integral: %3D a +32 dx x + 2

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Q: SSy'e»-'dy

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Q: Consider the integral -4 dx If the integral is divergent, type an upper-case "D". Otherwise,…

A: We need to check if series is divergent.

Q: Use the Trapezoidal Rule to approximate the integral of e^(3/x) dx from 2 to 3 with n=4 . Round the…

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Q: Evaluate the integral 8 dx x² V25 – x2 Note: Use an upper-case "C" for the constant of integration.

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Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral…

A: Here the lower limit is π4 and upper limit is π2

Q: Evaluate the integral. (Use C for the constant of integration.) dx cos(x) – 1

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Q: Calculate the approximate to the integral -5 (24 +2x² − 3)dx, by the composite midpoint rule with…

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Q: 20 Evaluate the integral dx dy by reversing the 4. order of integration. NOTE: Enter the exact…

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Q: Q:: A- Use Simpson's Rule with n=2 subintervals, evaluate the integral - Inx. dx , and compare the…

A: given integral :

Q: Evaluate the integral dx using Simpson's 1/3rd rule. Compare the error with the exact value. 1+x

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Q: Q4A) Find area bounded by y = 0, y = √x - x² using double integration.

A: We have to find area bounded by the given curve.

Q: Q1: Approximate the integral S dx with n 4 using the Simpson's rule. %3D 0 x+1

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Q: When using Simpson's rule to approximate the integral In(x+1)dx, then the upper bound of the error…

A: Consider the given information. I=∫23lnx+1dx Let's take 1 for n for the error bound. Calculate the…

Q: Using the trapezoidal rule with n = 4, estimate the integral / (x (x+1)² dx.

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Q: Using the trapezoidal rule with n = 5, approximate the integral L' TO S³ give the error of…

A: Trapezoidal rule formula: ∫abf(x) dx=h2(y0+yn)+2(y1+y2+...+yn-1) Given ∫03dx16+x2 Here f(x)=116+x2…

Q: Evaluate the integral - T/2 (8 + 4cosx)dx 0. Using:

A: The given integral is ∫0π28+4cosxdx In part (a), we shall solve it analytically, and in part (b), we…

Q: Q3: Evaluate the integral f xe dx by first finding the Maclaurin approximation to the integrand with…

A: The Maclaurin series: fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+… Where centered at a=0 or x=0. Given:…

Q: Evaluate the integral dx using Weddle's rule. o e-1

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Q: Determine h and N to approximate the integral e- dt within an accuracy of G = 10-5 using the (i)…

A: ii)  Equation is f(x)=exp(-x2).The value of the table for x and y x 0 0.25 0.5 0.75 1 y 1…

Q: 20 Evaluate the integral dx dy by reversing th order of integration. NOTE: Enter the exact answer.…

A: The integration of the integral is ex^2dxdy limit from y/4 to 5 and 0 to 20. Repost the 2nd image.

Q: 3. Change the order of integration sin dydx. Hence, evaluate the integral. y

A: Sol ∫0π∫xπsinyydydxChange order of integration =∫0π∫0ysinyydxdy

Q: 3.a) Apply the Trapezoid and corrected trapezoid rule, with h =, to approximate the integral £mcx+…

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Q: •20 Evaluate the integral dx dy by reversing the order of integration. NOTE: Enter the exact answer.

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Q: Q7. Using Simpson's Rule evaluate the integral (√x+1) dx using 8 subintervals.

A: In this question,  we have to evaluate the integral ∫08x+1dx using 8 subintervals by Simpson's Rule.

Q: Use the Trapezoidal Rule withn=4 steps to estimate the integral. 3 16) dx Use Simpson's Rule with n…

A: 1.  According to the Trapezoid rule,…

Q: Q1) Using numerical integration to estimate the area (r=4 )and c(4,0) with n=4 of the semicircle

A: Trapezoidal rule: One of the most significant integration rules in Calculus is the "Trapezoidal…

Q: Consider the integral -4 dx x2 If the integral is divergent, type an upper-case "D". Otherwise,…

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Q: The upper bound of the error when using Trapezoidal rule to approximate the integral 5 S xe*dx is хе…

A: The given integral is,∫25xe-x dx