Approximate the following integral using a) the composite trapezoidal rule with 10 points (use your Matlab script) b) the composite Simpson’s 1/3 rule with 10 points (use your Matlab script) ∫ (8 + 4cosx)dx 0 to pi/2

Q: Evaluate the following integrals using (a) Trapezoidal Rule and (b) Simpson Rule by finding n such…

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Q: Use any method to evaluate the integrals ∫cot x/cos2 x dx

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Q: The integral S dydx represents what?

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Q: Use Adaptive quadrature to approximate the following integral to within 10-5 ! (x + sin4x)dx 1

A: Given: The equation is ∫12x+sin 4xdx

Q: Make a substitution to express the integrand as arational function and then evaluate the integral.…

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Q: Calculate the following integral by Simpson's method 3/8 with n= and verify the error obtained. In…

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Q: Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule. Estimate…

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Q: Approximate the following integral using three-point Gaussian quadrature rule. 2 dr 1²–4

A: Gaussian quadrature rules evaluates the integral with higher accuracy. The three point Gaussian…

Q: By using trapezoidal rule, n=2, The integral = π/2 sin (x) dx 0.9444 O 0.9481 O 0.94809 O 0.9482 O…

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Q: [ V4-x² dx

A: We have to evaluate the integral using fundamental thero

Q: |1+cos ydy

A: Let I=∫1+cosy dy

Q: evaluate the definte integral 4 at the top and 1 in the bottom square root of y+1

A: Given,         The integral 4 at the top and 1 in the bottom square root of y+1.

Q: Use Simpson's Rule and the Trapezoid Rule to approximate the value of the following integral using 4…

A: The given integral is ∫0π2cosxdx. Here, the interval of integration a,b=0,π2 and the function is…

Q: 3) a) Use Simpson's rule with n=4. b) Estimate the error in the approximation. -2x dx jedx to…

A: Given integral is ∫06e−2xdx. a We have to approximate the given integral by using Simpson rule.…

Q: Use Adaptive quadrature to approximate the following integral to within 10^-5

A: Let fx=x+sin4x. First, apply Simpson’s rule for n = 2. Simpson’s formula for a sub-interval of xi,xj…

Q: Approximate the following integral using three-point Gaussian quadrature rule. 1 rp-

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Q: Evaluate the integral * cosh? dx -In 2

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Q: use the trapeziodal and semson rule to approximate the following integrals

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Q: Use Trapezoidal and Simpsons 1/3 rule to estimate integral ( - 2x° + 7x - 5) de.

A: The expression ∫13x3-2x2+7x-5dx. We have to use Trapezoidal and Simpsons 13 rule to estimate the…

Q: use an appropriate substitution and then a trigonometric substitution to evaluate the integrals.

A: Evaluate: ∫1-(lnx)2xlnxdx

Q: Evaluate the definite integral using the Newton-Cotes quadrature formula (Trapezoidal Rule and…

A: According to the fundamental theorem of calculus ∫abf(x)dx=F(b)-F(a), where  dFdx=f(x). The function…

Q: Use trapezoidal and Simpsons rule to evaluate the integral given, by taking n=6 and h=1

A: Given that, the integral is ∫01x+21-x2dx and n=6. Obtain the value of ∆x=b-an. ∆x=1-06=16 Divide the…

Q: Graph the integrand and use areas to evaluate the integral. 7) V49 - x2 dx -7

A: Given:   Compare the above equations, Therefore, the above equation is the equation of the circle…

Q: Graph the integrand and use areas to evaluate the integral. V 25 – x² dx - 5

A: Given,          ∫-5525-x2dx

Q: Graph the integrand, and use area to evaluate the definite integral dx. x IN 2.

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Q: evaluate the integral (Usec. af nitegratun) for the constant बदेशव 1ehan) 5x cos (8x) dx

A: Given

Q: Use reduction formulas to evaluate the integrals ∫ 8 cot4 t dt

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Q: Use the indicated entry in the Table of Integrals to evaluate the integral. 3V 4x2 – 3 dx; entry 39

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Q: Approximate the integral 1∫0x3dx using the Trapezoidal Rule with n=2 subintervals.

A: We need to approximate the given integral using the Trapezoidal rule with n=2 subintervals.

Q: Evaluate the integral: V3 S arctan () da *Input answer as decimal round-off to 2 decimal places.

A: Given :∫13arctan1xdx

Q: Use the Midpoint Rule to approximate the integral 15 (-læ – 3a?)da with n=3.

A: Given,  ∫715(-1x-3x2)dx

Q: :6. Bet“ dt.

A: (6). Given: I=∫t3et4dt   ...1   We know that; ∫eax+bdx=1aeax+b+C   Note; As per Bartleby guidelines…

Q: What is the value of the approximation of the integral So (1 - e-2) dr using four-segment…

A: Using the formula  ∫abf(x) dx ≈b-a2n[ f(a) + f(b) + 2 ∑i=1nf(a+ih) ] where h = b-an,  n = number of…

Q: Approximate the integral S" x² sin x dx by Trapezoidal rule with n = 4. O Find the minimum n…

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Q: The first short computation of the integral of secθ is due to Isaac Barrow. Adapt his computations…

A: Isaac Barrow did the integral of sec(θ) as follows: ∫sec(θ) dθ=∫sec(θ)sec(θ)+tan(θ)sec(θ)+tan(θ)dθ…

Q: Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule. Estimate…

A: Given integral is ∫13 2x-1 dx Take fx =2x-1 Number of steps = 4 Step size h = 3-14 =24=12=0.5 So, h…

Q: |(3x3 – 2x² + 1) sinh 2x

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Q: evaluate the integral using the methods covered in the text so far.

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Q: Compute the approximation  of the integral -4 to 4 e^(-x^2) using mid points with 4 rectangles, you…

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

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Q: Evaluate the integral of cos^2 ydy

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: The area bounded by the small loop of the limaçon r = 1 – 2sin0 is given by the definite integral

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Q: Compute the following integrals using the guidelines for integrating powers of trigonometric…

A: Please refer to the image below

Q: Approximate the integral V1+ x³dx using:

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Q: Consider the integral 2x x² dr. Use the composite Trapezoidal rule with n = 4 to approximate the…

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Q: Use the trapezoidal rule with n=6 subintervals to approximate the integral 1 to 4  ln(x+sqrt(x)) dx.

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Q: 1.a) Apply the Trapezoid and Corrected Trapezoid Rule, with h =, to approximate the integrale-2x²…

A: (a). Given integral is ∫13e-2x2dx. The step size is h=18. We know that the integral of a function fx…

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

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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.