16 Evaluate ſ," x²In 3x dx correct to three decimal places.

Q: Evaluate the 3 dx entegral cas/int) dk Sxtl

A: To integrate the given expressions.

Q: 1 (a) Calculate the value of Jo dx correct to 3 significant figures taking six intervals by…

A:

Q: Evaluate o S ) dyda by choosing the order of integration. Round your answer to three decimal places.…

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Q: Estimate | (2x – 5) dx using left endpoints for n = 3 approximating rectangles. %3D 5 (2x – 5) dx is…

A: Given: ∫152x-5ddx The left Riemann sum (also known as the left endpoint approximation) uses the left…

Q: 76. Use integration by parts to obtain the formula VT=* dx = +VT=x + 1 dx. 1 – x?

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Q: ) 「ざs")dx

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Q: Estimate sinx? dx with an error of less than 0.001.

A: Given ∫01sin(x2)dx

Q: 53. Find the value of 1 dx using weddle’s rule. 1+x?

A: Weddle's law is a formula for solving numerical integration.

Q: Calculate the deriv L tan2tdt d_ dx II

A: Derivation of          is calculated as shown below

Q: Evaluate 11 2 By (+³+1)2 dx dy 24 by reversing the order of integration

A:

Q: 52. Use Property 8 to estimate the value of the integral 1 dx Jo 1 + x2

A: Given: Integration 0 to 2 of (1/1+x^2).dx

Q: Evaluate the integral.

A:

Q: Differentiate the following function. y = 3 In x + In 4 d -(3 In x + In 4) = | dx

A: If you like the solution then please give it a thumbs up.... The Answer is:           Result :    3…

Q: Evaluate thl integraus in H3) dx (44) dx dx 17 +x? 45

A: Disclaimer:  Since you have posted multiple questions, I will answer first three questions. If you…

Q: Find the most general antiderivative or indefinite integral. 6 5 dt

A: The given integral,          ∫tt56+t3t2dt

Q: Evaluate I ta tanh x ln(cosh x) dx.

A:

Q: late the generalized integral. , (1+

A: In general, the integral of a real valued function  f(x) with respect to a real variable x on an…

Q: Show that (In kx) dx (In x), where x > 0 and k is a positive dx real number.

A: ddxln kx=ddxln x, where x>0 & k is a positive real number.

Q: Find the most general antiderivative or indefinite integral. dx

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Q: Find the indefinite integral.

A:

Q: Use Simpson's rule with 3 8 intervals, to evaluate 2 dx, correct to 3 decimal places.

A:

Q: Evaluate A Se-* dx by Simpson's 1/3 rule with n=10, work for six digit

A:

Q: Evaluate the integral: e3+ cosh2x33 + cosh2xsinh2x dx

A:

Q: Evaluate the integral: S2 (2x + 6) dx Input answer as decimal. Round off to 2 decimal places.

A:

Q: =valuate the integral. (Rem. 25 + x2 dx

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Q: 5. Evaluate x + v1 – x² dx by interpreting it in terms of areas.

A: We have to consider it as sum of two functions.

Q: Find. d? (® Int) dt

A:

Q: The area under the curve y = cos x from x = a to x = is 0.2. What is the value of a 2 rounded to…

A: Area under a curve y(x) is given by ∫abydx         where a≤x≤b

Q: 25 dr. valuate the integral: re

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Q: 16 Evaluate x*In 3x dx correct to three decimal places.

A: Given that, ∫12x2ln 3x To find- The value of the above integral. Concept Used- The above integral…

Q: 15. Use the table of integralsto evaleuate, the integral. ex dx

A: We have to evaluate the integral ∫ex1-e2x32dx by using the table of integrals.

Q: 17. Find the integral of ((x^4)/((x^2)+7))dx

A: Given: Let I=∫x4x2+7 dx To Find: To evaluate the given integration

Q: cln 2 tanh 2x dx

A:

Q: Q2]Using Simpsons1/3 rule for evaluation of sinh(e-*) dx use n = 4 andwork to 5 decimal place?

A:

Q: Estimate (2x – 5) dx using midpoints for n = 3 approximating rectangles. (2x – 5) dx is…

A: 4

Q: 10Evaluate the integral 2TT ex ス

A:

Q: Evaluate 0, dx by dividing the interval into 10 equal parts 8х-5 by using Simpson's one - third…

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Q: 2) By compating aderivatives, find the Tay ior for tixl= la x at

A: By using Taylor series expension of lnx

Q: What is wrong with this calculation? 1 dx In |x||, = In 1 - In 1 = 0 - 1

A: The integral of 1xwith respect to x is log(|x|). where x≠0, cause if it is zero then function became…

Q: 1 point) Calculate the integral: 1 dx = (x + 8)(x + 4)

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Q: Evaluate dx using Simpson's rule. 3

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Q: 7) Estimate the value of e dx using Simpson's rule using 8 subintervals.

A: Given: ∫02ex2dx Here, n = 8 subintervals

Q: 8. 1 dx, x In x

A: Given data:     The given integral is: .   Convert the above integral into indefinite integral.…

Q: Evaluate   ∫01 (x  +  √(1 -x2)) dx   by interpreting it in terms of areas.

A: Given integral, ∫01x+1-x2 dx

Q: 1. cosh (j) 2. tanh 3. 3. In(2 + j3)

A:

Q: Use property 8 to estimate the value of the integral 1,12 15/0 - 58 a dx.

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Q: •8 1 dx /1+ x 0.

A: Substitute 1+x = t2 but don't change the limits and solve the integration.

Q: 16. Evaluate x + v1- x² dx by interpreting it in terms of areas.

A:

Q: Evaluate the integral. „ 3X + 7 e ~×) dx , 3× + 7 e ~×) dx =

A:

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.