Approximate sin(x) dx using a Riemann sum with n 3 terms and the midnoint rule.

Q: Determine if the improper integral | (x+2)* 12 dx converges or diverges. If it -8 converges evaluate…

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Q: 3. Find the fourth-order Taylor Series approximation of y = cosx + sin x at x = 0.1 on the basis of…

A: Here, we need to find the fourth-order Taylor series approximation of y=cos x+sin x at x=0.1 on the…

Q: Calculate the value of the function f(x) = sinx cosx at  x= 0.1 using the 4th order derivative…

A: Suppose fx is n times differentiable function then nth degree Taylor approximation for fx near 0 as…

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: Determine whether the integral converges or diverges. If it converges, determine its value. dx L…

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Q: Q3) Use Riemann sum to evaluate the definite integral: 2 | (2x + 1)dx where n = 0.4

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Q: Find the indefinite integral. (Use C for the constant of integration.) cos5 t dt sin t

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Q: Find "(x2 + 3)dx using the definition of definite integral (i.e. using a limit of Riemann sums).

A: Solve the following integral

Q: 3. Determine the number of sub-intervals required to approximate 3 -x² dx e using the Trapezoid Rule…

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Q: use the elimnaton method zhみみ人みメ differential equeti cns

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Q: Use numerical integration to estimate the value of 0.6 sin- 0.6 dx VT ī – x For reference, sin 0.6 =…

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Q: 3. Find the indefinite integral. (Use C for the constant of integration.) Ssin(3x) cos(3x) dx

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Q: 5) Approximate x²-1|dx with a right-endpoint Riemann sum using four equal subintervals.

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: solve the integral: I3=integral limit from 0 to positive infinity 1/(4e3x+7) dx

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Q: Find the indefinite integral. sinh(2 – 7x) dx Step 1 First, let u = 2 - x. Now, differentiate u with…

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Q: Use series to approximate the definite integral S xcos(x²)dx . (Give your answer correct to 10-3)

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Q: provide the steps for f(x)= sin x2/ x.     integrate using power series

A: We have to find the integrate by using poer sereis

Q: Find the indefinite integral. sinh(4 - 7x) dx Step 1 First, let u = 4 - x. Now, differentiate u with…

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Q: S°(xe* + 1)dx

A: In this question we have to solve the given integral by using some of the newton-cotes rule.

Q: Approximate the integral using Taylor series method: x• cos?x dx EIN

A: Write the Taylor series for cos2x.

Q: Make an octave code to integrate ex with respect to dx from 0 to 1, by Simpson’s ⅓ rule. Divide the…

A: Equation is f(x)=exThe value of the table for x and y x 0 0.25 0.5 0.75 1 y 1 1.284 1.6487…

Q: Evaluate the integral. (Use C for the constant of integration.) fu- (x – 3)sin(Tx) dx

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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: Find the indefinite integral. (Use C for the constant of integration.) .5 cos dt sin t

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Q: -dx converges or diverges. Justify your claim. determine if the integral 1+ cos? r

A: Introduction: When the integrand becomes discontinuous at any of the limits of the given…

Q: Find the indefinite integral. sinh(8 - 9x) dx Step 1 First, let u = 8 - x. Now, differentiate u with…

A: Explanation of the answer is as follows

Q: Explain why the improper integral (x + 3) sin(x) dx L. (x² + 1)(x² + 4)² is convergent. 8

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Q: (a) Integrate the following definite integrals by using suitable method: (i) S tan-1 x dx

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Q: Evaluate the integral -21 cos(-2t) dt Note: Use an upper-case "C" for the constant of integration.

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Q: 2 To approximate (x – 6)* dx using Riemann sum, the partition of 4 subintervals each length 2 are:

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Q: of P converges Find the Value which the integral absoluley condition. Sin () dx

A: To find the value of p for which the integral ∫1∞sin(1x)xpdx  converges absolutely. The improper…

Q: x2 dx V49 -x2 or diverges. Determine whether the improper integral converges

A: Improper integral.

Q: .5 Estimate the middle Riemann sum for 1 dx (n= 4). 3 1-lnx

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Q: evaluate the indefinite integral 3+ -dt. Use C for the constant of integration.

A: Given : ∫3 + 1t61t2dt

Q: Evaluate the integral if it converges and enter the exact value. If the integral diverges, indicate…

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Q: Give the Riemann sum approximation for the definite integral S° dx using n = 4 subintervals and left…

A: Left reimann sum

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: Jcos(2x)+ sin(0.5x) Using riemann compute for the integral of F(x) = tan(3x) sum over the interval…

A: We can solve this using Riemann sum

Q: Determine whether the improper integral diverges or converges. Sº cos(10x) dx converges O diverges…

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Q: 1. Find fe- cos(x)dx. 2. The following improper integral converges. Compute it using part 1. e*…

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Q: 0 In x dx converges or diverges. If Determine whether the improper integral it converges, find its…

A: Given that a integral and we find its value and check the integral diverges and converges. We know…

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) ecos(25t) sin(25t) dt

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Q: Evaluate the indefinite integral 4(1 + tan(t)) sec2(t) dt Note: Any arbitrary constants used must be…

A: We need to calculate the integral: I=∫41+ tan t5 sec2t dt This integral can be evaluated as follows:

Q: Use Romberg integration to approximate √² 2x² + x − 1 dx. Compute the Romberg table until Rij-…

A: The Final diagonal element is always consider the best estimate of the integral  I=∫abf(x)…

Q: How would I find the UPPER Riemann sum when n=6 for sinx over the interval [0,pi]

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Q: 1 cos x³dx -1 a. Use Simpson's rule to approximate the following integrals: (using n = 8…

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Q: cos(x')dx

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Q: Evaluate the integration - 1 I = cos(3x)– 5 dx with h=0.4, Using 3/8 Simpson Rule. Write your answer…

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Q: Evaluate the definite integral S (1 + 2x) dx using Riemann sum.

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Q: V2x + sin? æ Determine whether the improper integral dx converges or diverges cos? x

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.