Prove That:- o sinhz= loy (Z+lz*+l )

Q: 2Sin Cze) 4-COS S (zt)

A: The solution for the above question is as shown below.

Q: Evaluate the integral. * T/3 3 sec 0 tan 0 de In/4

A: Given that the integral is ∫π4π33secθtanθdθ. It is required to evaluate the given integral…

Q: 2. Use Cauchy's Integral formula, Evaluate the following sin42 IZ1= 3. (Z-4)3

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

Q: 5. Use the binomial expansion and Cauchy's Integral Theorem to evaluate ( с 2n dz Z + -/-/-) where C…

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Q: Use the Fundamental Theorem of Calculus to evaluate (if it exists) -5t- dt. If the integral does not…

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Q: Use a substitution of the form u = ax +b to evaluate the indefinite integral belov 7x+1 dx 7x+1 dx%=

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Q: Evaluate the iterated integral: a " cos(2) dy dar.

A: The iterated integral is given as:…

Q: Evaluate the definite integral exactly, using the Fundamental Theorem. 6. 1 -dt 1 dt II

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Q: Find the definite integral using the Fundamental Theorem. 2 1 dt 4t NOTE: Enter the exact answer. ~2…

A: Definite integration problem

Q: Evaluate the impropec integral oc sho that it diverges, dx

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Q: Evaluate the definite integral exactly, using the Fundamental Theorem. 1 dt 72 1 dt 12 %3D eTextbook…

A: ∫151t2 dt

Q: Use the substitution æ = 2 tan(0) to evaluate the indefinite integral 4dx V + 4

A: NOTE: Refresh your page if you can't see any equations. . ...............(1) substitute…

Q: Use the Fundamental Theorem of Calculus to evaluate (if it exists) 4t-5 dt. If the integral does not…

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Q: 4. Compute f'dr by using fundamental theorem of integral calculus.

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Q: Find antideriuative Flx) of the an flx) = _8 sinx 13 + COSX functian such that FlO) = 1 %3D %3D

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Q: Evaluate the improper intergal 1 dr using the residue theorem. (x² + 4)?

A: Solving imroper integral using residue theorem

Q: and let ah -(-1'I Let In tan (a) for n = 0,1, 2 Intz 1) Show that In + Io+ り+! (-1)" for nal an-…

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Q: Evaluate the integral. zp zul s)

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

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Q: Evaluate the integral 9t tan (1) dt

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Q: . Use Taylor's neries, to prove that ein z tan (x+ h)3tan" % + (h sin z). sin 3z sin 2z + (h sin zj…

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Q: [(9)se x². d²+xdx + (x²-n²) y=0_ by substitution x== 1102 at 2 pt souhen Hence show that it has no…

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Q: 2. Use Cauchy's Integral formula, Evaluate the foll D I - & tantz Z² C: 171=1

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Q: Scos -de cos

A: We have to evaluate the integral ∫cos3θ3dθ.

Q: Use the given substitution to evaluate the integral.

A: Given integral: ∫sec22θ tan2θ dθ

Q: (4 b Prove that 5 foxx dx = K (6-a) using definition of integral, where fø= k [a,b], on

A: Given function is fx=k on a,b. We have to prove that ∫abfxdx=kb−a. Take Left hand side  Use Property…

Q: Determine the convergence of the integral 2 tan x UTM UTM dx. (In(cos x) GUTM

A: Given: ∫π3π2tanxlncosx2dx

Q: Use this result to either evaluate the improper integral +oo 5xe dr or show that it diverges.

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Q: Evaluate the integral. (Hint: u-sub) sec x tan x dx 5+ sec x O 5 In Isec xl + C O In 15 + sec xl + C…

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Q: Se* sin 2xdx

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Q: "(2 - sinoy de

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Q: Evaluate the following integral JI (1 – (x + y))dA where T is the triangle with vertices (0, 0), (1,…

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Q: de 1+tan 0 k/2

A: Let I=∫0π2dθ1+tan θ      I=∫0π2dθ1+sin θcos θI=∫0π2cos θ dθcos θ+sin θ     ....(1)Using property…

Q: cos'xsin*xdx IN

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Q: Q5. Usung Maclaurin's thcorem expand, 5tanx as þar as +he term containing x". QC. Prove that , sinx…

A: A Maclaurin series is given by f(x) = ∑k=0∞fk(0)k !xk Given function f(x) = x5 tan x     Here, each…

Q: Evaluate the integral. S coth 7x) dx A) In sinh 7x *C B) In lanh 7x +C © } csch' 7x + C 7 In

A: The given integral is ∫coth7xdx.

Q: Use the form of the definition of the integral given in Theorem 4 in section 5.2 to evaluate the…

A: First integrate the function x2+7 with respect to x using the power rule of differentiation.

Q: Is Ź U Ź,asigma a lgebra over X? 4. Prove your an swer.

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Q: In (xle)secx (2- sec²x) ha sec(3A – x) Ju"du? What should be the value of A for dr to be integrable…

A: Note -  Acc. to Bartleby guidelines, we are supposed to do only one question . If you want more to…

Q: 1 -) Prove the existence of the improper integral 1 (In x) sin – dx -

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Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

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Q: (10x – 3x + 1)dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Use Cauchy's Residue Theorem to compute the improper integral (x + 3) sin(x) dx (x2 + 1)(x² + 4)2 00…

A: Given that ∫-∞∞x+3 sinxx2+1x2+42dx Using Cauchy residue theorem, we can written it as ∫-∞∞z+3…

Q: Show that In xdx = x In x-x+C and use this result to determine the integral:

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Q: Prove that tan'z= leto 1/2 in (1+2) tan't z • tanw=Z Z = Sinw cosw

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Q: Solve in terms f Bessel's functrom the folowrng (z=) DES?

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Q: Evaluate the integral: 7/20¹² sin (1) dt du

A: Follow the procedure given below.

Q: sec(2 In x) tan(2 In 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.