Q2/ Find the dirivative for the follwing function y = cosh(x)/ln(x)

Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx.

A: Given integral is ∫03 x3+xdx Number of sub-intervals = 6 Take f(x) = x3+x Step size  ∆x  = 3-06…

Q: Evaluate the integral. (Use C for the constant of integration.) x5 dx

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Q: 3) f(x) = (x + 4) Standard form: Y-int:

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: Evaluate the integral. (Use C for the constant of integration.) dx - x2

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Q: Evaluate the qwen Detinite Integra ax(7-x²)* dx 2X

A: From the given integration: I=∫-3-22x7-x23dx.....(1) Using the substitution method to calculate the…

Q: 3) Estimate Y(2) using Euler's method with 0.5 long dY intervals. Y - 2X and Y(1) = 0. dx

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Q: Evaluate the double integration: e²x e dxdy

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

Q: se the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx.

A:

Q: Determine h(x) = -x3 t 1ocal eXTrema for + 4x² t48X +9 USing the first derivatve Test,

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Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x3 +x)dx

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Q: Let f(x) = x sin(2 x). Find its average value for 0sxs/2.

A: Given the query is to find the average value of function over the interval [0,π/2].

Q: (a) Use the Midpoint Rule with n = 6 to approximate integral S³ dx 8 x-6 6 x+8

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: x2 dy dx by reversing the order of integration. 4/x 1. Evaluate

A: Given double integral is∫14 ∫4x4x2 dy dxNow , By interchanging the integral we have ,∫y=14…

Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx

A: We need to use the mid-point rule to find the value of the definite integral.  The mid-point rule…

Q: (ii) Integrate the following function by the method of integration by parts: fx* In x dx

A: Details solution is given below :

Q: evaluate the definity integral  from -10 to 10  (2 - x)dx

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Q: Use integration by parts to find the antiderivative of f(x) = ln(x).

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Q: Differentiate y = In(cosh x) + 2 cosh x O a. sechx (1 cosh O b. cosh x cosh a 2 O c. sinh x с. cosh…

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Q: Q3) Reversing the order of integration 2 y² sinxy dy dx

A: Explanation of the solution is given below...

Q: (a) Use the Midpoint Rule with n = 6 to approximate integral 8 x-6 S8 dx 6 x+8 ?

A: As per the instruction, we will be answering the first question. Given:

Q: 3. Use properties of integration to evaluate S, x³Vx* + 5dx. If necessary, round your answer to four…

A: Given : ∫12x3x4+5dx   The Answer:   13.5895

Q: Evaluate the integral. (Use C for the constant of integration.) (arctan(x))5 | x2 + 1 dx

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Q: Evaluate (indefinite integral) (4x^2.5 - x^e - 2sinx)dx (t^3 + 5t^2 - 4)/ (t^2) dt

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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 f x³e2x dx using integration by parts

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Q: Q3] Use the trapezoidal rule of integration to determine the value of S, xlnx dx with h = 0.1, work…

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Q: Find an antiderivative for f(x) = lxl.

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Q: Find the indefinite integral. (Use C for the constant of integration.) dz zV 49z2 - 9

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Q: Find the most general antiderivative of the function. ( Use C for the constant of the…

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Q: (x² cosh(sin(x-y))= intx-vn) = X' dy 9.

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Q: S x² e¹x dx

A: EVALUATE USING INTEGRATION BY PARTS  For the function x2e4x .

Q: 2: Change the order of integration. •ln 4 f(u, у)dydx.

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Q: Evaluate the integral. (Use C for the constant of integration.) х dx x2 + x + 3

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Q: 2. se integration by pacts to eval integralig x² In (3x)dx niz

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Q: (b) YOUR TURN 4 Find dx. Vx f(x) deriv for in

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Q: d) Evaluate using integration by parts: [(x+2)ln x dx

A: Integration by parts rule:

Q: dx ах VX

A:

Q: find the derivative y= the integral from 0 to the square root of x 5tcos(t^4) dt show all work

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Q: Use order of h8 Romberg integration to evaluate xe2x dx

A: Let us start solving and find et value

Q: CoSx b) F(x) = Int dt

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Q: fil experini for dy txďn

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Q: Evaluate e" dydx by reversing the order of integration. x/3)

A: A detailed solution is given below.

Q: Sx* (4 – x)* dx

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Q: 2. Use the Midpoint Rule with n = 4 to estimate (x² + 1) dx %3D

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Q: a) Evaluate 1| dx by using integration by parts.

A: Dear learner, as per our guidelines we can provide the solution for first one only. Kindly post…

Q: sinh x – 1 dx cosh x

A: The given integral,        ∫sinhx-1coshxdx

Q: Let y = 5(square root x) Find the change in y. Delta-y when x = 5 and delta-x = 0.1 Find the…

A: The given function is y=5x. We need to find ∆y when x=5 and ∆x=0.1. Also, to find dy when x=5 and…

Q: 3. Estimate the value of the integral 1 dx (n = 4) using Trapezoidal rule. 1+ln x

A: The value of h in the trapezoidal rule is h = b-anh = 5-34h = 24h = 0.5 Form a table with the x…

Q: 4) First make a substitution and then use integration by parts to evaluate the integral. (Use C for…

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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.