The approximation of I = S, tanx dx using composite Simpson's rule with n=5 is: O 0.6158 O 0.6236 0.6165 O None of the choicr

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

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Q: Evaluate J by means of Simpson's rule with n = 2m =20 and h =0.05 J= exp(-x²) dx Answer in 4 decimal…

A: f(x)=exp(-x2)h=b-an=1-020=0.05 table for x and y value: x 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4…

Q: Calculate the integral approximation S12 for Si ²1 dx. +1 S12 =

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Q: Find General Solution on this Diffential E Qution by using (uC set) =e +Sin X

A: Given differential equation is y''+y'-2y=ex+sinxfind the general solution

Q: (2.5 + 3.8x? – 1.6x³ + 14.2x5 – 8.1x)dx

A: To Evaluate the following integral: I=∫13(2.5+3.8x2-1.6x3+14.2x5-8.1x6)dx a) analytically; (b)…

Q: Evaluate the following integral. tan x sec *x dx X, V tan x 4. sec 'x dx = (Type an exact answer.)

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Q: Evaluate the integral (2cos0+5cos 30)* sin0 d® using Simpson's 3/8 method and dividing the 4. whole…

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Q: Use the method of substitution to calculate dx. + x² O a. In|æ|+C O b. In |1+x2| +C O c. arctan(x) +…

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Q: The approximation of I = tanx dx using composite Simpson's rule with n-5 is: O 0.6165 O None of the…

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Q: Find the indicated Trapezoid Rule approximation to the following integral. .3 5 sin 3* dx using n =…

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Q: (b) Evaluate 1 dx using Romberg's S. 1 + x2 hence obtain an approximate value of T.

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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: O Approximate So In (3 + sin x)dx using Simpson's Rule with(n = 4 %3D

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Q: 5. Evaluate the following integral: S/3x tan?(x) dx (Hint: Use a substitution first)

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Q: Use Simpson's rule to approximate the following integrals: (using n = 8 subintervals a. cos x³ dx

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Find the approximate area under the curve of f (x) =cos (5) from x = 0 to x = TT, using 4…

A: Here, the interval [0,π] is divided into 4 intervals of the length of each interval is ∆x=π-04=π4.…

Q: In  the given question as folows use Taylor’s Theorem to obtain an upper bound for the error of the…

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Q: lower bounds Ror o.5 dx dud よx 0.5 Add the se to arrive at am improved estimate of

A: Find upper and lower bounds.

Q: ) Evaluate the following integral: S V2 + sin 3t cos 3t dt

A: We have to find solution of given integral.

Q: Evaluate 2 dx Using Simpson's 3/8 Rule,taking (h=0.2). Answer:0.80674

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Q: of the ):305t=2 ;find at t:2 the area riDole

A: Given radius function is  r(t)=30t+2

Q: The approximation of 1 = cos(x+10) dx using composite Simpson's rule with n-3 is: 1.01259 3.25498

A: In this question, the concept of Integration is applied. Integration Integration is a method of…

Q: Evaluate the following integral: f*(1-e^³)dx d. Composite trapezoidal rule, n=4 e. Simpson's 1/3…

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Q: Evaluate the following double integral sin (y) dydr

A: To evaluate the integral

Q: Evaluate the following double integral (x², coS y – sin x)dxdy.

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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: Estimate the integral sin (x) dx by Simpson's rule using n= 4. а) 0.12082 b) 00.06041 c) 0.0863 d)…

A: Option c is the correct option.

Q: 2 | (8 + 4 cos 2) dæ

A: In this problem first we divide the interval into equal subintervals and the width of the…

Q: The approximation of 3x e sin(2x) dx by Simpson's Rule is 2.584696

A: We have, ∫0π4e3xsin2xdx Let Number of subintervals be 30.…

Q: Find cosh r In(sinh a)dr.

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Q: Evaluate the following integral : S (sec X + cot X)² dx

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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: The approximation of the integral (x - 5)'in(x + 5)dx using two points Gaussian quadrature formula…

A: We have to evaluate ∫-11x-52lnx+5dx using the two-point Gaussian quadrature formula. Now, 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: Evaluate the following integral: fa-e²¹) dx a. Analytically b. Trapezoidal rule c. Composite…

A: The given definite integral ∫041-e-xdx use the integral formula, ∫dx=x+C∫eaxdx=eaxa+C

Q: J= * By using trapezoidal rule, n=2, The integral π/2 0 sin (x) dx 0.9482 O 0.9480 O 0.9481 O 0.9444…

A: The given problem is to find the approximate value of the given definite integral using the…

Q: 4. Evaluate the following integral: S tan3 x dx

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Q: Identify the appropriate substitution for the following integral: Sesin z cos adx

A: Assume u=sinx then du=cosxdx. Substitute sinx=u and cosxdx=du in the given integral.…

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

A: Solution

Q: 1. Evaluate the following integral: (6 + 3 cos x) dx a. Analytically b. single application of the…

A: In the Trapezoidal rule, we calculate the area under the curve by dividing the area into the smaller…

Q: Evaluate J by means of Simpson's rule with n = 2m=10 and h = 0.10 = [*exp(-x²) dx Answer in 4…

A: f(x)=exp(-x2)h=b-an=1-010=0.10 table for x and y values x 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1…

Q: c) Determine the number M and the interval width h so that the Trapezoidal rule for M subintervals…

A: The objective is to find the number M and interval width h such that Trapezoidal rule Tnf for M…

Q: Use the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+37) -dx, 1+x?

A: According to the fundamental theorem of calculus ∫x0xnf(x)dx=F(xn)-F(x0), where dFdx=f(x). The…

Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

A: ∫0π22cos4xdx,  n=4Then ∆x=π2-04=π8The subintervals are 0,π8,π8,π4,π4,3π8,3π8,π2By midpoint…

Q: Use the Composite Trapezoidal rule with the indicated values ofn to approximate the following…

A: As per bartleby guidelines we only give first question answers.

Q: Use a double integral to find the area of one loop of the rose r = 2 cos(30).

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Q: Evaluate the integral cos (x) sin(x) dx 13 using the substitution u = cos(x). cos(x) sin(x) d.x ,13…

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

Q: Evaluate the following integral: f*(1-e²³)dx a. Analytically b. Trapezoidal rule c. Composite…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: The approximation of I = tanx dx using composite Simpson's rule with n=5 is: %3D O 0.6236 O 0.6158 O…

A:

Q: Determine the following convolutions by integration (a) 1 * sin wt (b) et * e

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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.