Compute for the value of tanh-(1 – i) In 5 my + 2.13i In /2 + 2.13i Inv - 4.25i 2 In /2 + 2.13i

Q: 1. Evaluate the integral: 2³ cos (dt du

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Q: 59. Show that for any number a > 1 -Ina In x dx + e dy = a In a,

A: Given: ∫1alnxdx+∫0lnaeydy=alna

Q: Compute for the value of tanh (1 – i) Iny + 2.13i In 2 + 2.13i 2 In 5 - 4.25i 2 In v2 + 2.13i

A: To Compute: tanh-11-i Concept: 1. tanh-1z=12ln1+z-ln1-z2. lnz=lnr+iθ+2nπwhere,…

Q: Use substitutions to waite (In t)at, for seyo (1n ms of と in 0,9 € N, aE IR E IN, a E IR, a#0 where

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Q: For which values of a does x + a = 0 have a solu­tion in Z5?

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Q: ハジ nd the exact lkength of the wnve र 4=1n(seccx)),

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Q: Evaluate the following integral. S 7. dz 25 16

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Q: Fmd the power series represedatia Fin of 和 Pn ant to tan't dt, fez)- where enD (B) (C) and an 2. and…

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

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Q: evaluate the integral fromn 0 to pi/2 (cosx)^3

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Q: Use the integral test to Σ cos 1/n n2 1 ך

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Q: QS) Use Simpson's 3/8 rule to compute the approximated solution wihere f (x) = ,deind a te interva…

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

A: We have to find solution of given integral.

Q: Evaluate the following definite integral ,-(s-2)t sin(3t) dt. 3 2 (8 – 2)2 + 9 (8 – 3)2 + 4 - - O 1.…

A: Properties of Laplace transform  Lf(t)=∫0∞e-stf(t)dt Leatsinbt=b(s-a)2+b2 Lsinat=as2+a2

Q: Evaluate the definite integral. 4 cos(πt/2) dt

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Q: Evaluate the integral: S/2 Se S77/2 S¹² sin (=) dt du π/2

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Q: Show dz 4 In= 는I미페 - for a<0. x <

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Q: ove that 1 cosh(tanh) = -1 -1 < r < 1. V1- 2

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Q: Evaluate the indefinite integral. 3 dt (t + 8)5 + C

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Q: he IVP d's (p² – 121) dp1 d's ds + s 1 = sin(p) dp3 p2 +1 dp s(7) = -994 ds = 19 dp l7 d's = 4 dp2…

A: Given the IVF (p2-121)d4sdp4+p4d3sdp3+1p2+1dsdp+s = sin(p)s(7)=-994[dsdp]7=19[d2sdp2]7=4[d3sdp3]7=10…

Q: O if Z= x'tan!Y final dž Handwriting Point Cl,!) In

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Q: Evaluate the integral 7sin^2(x)cos^2(x)dx, from 0 to pi/2

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Q: What is tanh (Ei) O V3 V3i O 13

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Q: Solve the following ODE dy + ty = ty? dt with the initial condition that y(0) = 0.5. %3D

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Q: Evaluate the integrals in Exercises

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Q: Evaluate the integral. 7/2 sin 8t sin 7t dt 16 O 31 O T5 3

A: the given integral is ∫0π2sin8t sin7t dt use the formula Sin C sin D= -cosC+D+cosC-D2 here C=8t and…

Q: 2 (b) S(2 + tan (0))do (c) S 2'(1 + 5')dt

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Q: sen( ds

A: We will find out the required value.

Q: 57. Use the substitution u = x/3 to prove dx 1942=tan 1+0 www C 9+x² 3 3

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

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Q: Find the indefinite integral.

A: Given : ∫tan2tt2dt

Q: Which of the following is one of the correct steps to evaluate cos3 dt to obtain the correct indef…

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Q: 16. Find he exact soution on The interval [0,2m] 25in?x ャ Bsinx +3= 0 5sinx t

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Q: Evaluate the indefinite integral. 5 dt (t + 7)³

A: Given: ∫5t+73dt we know that ∫dxx+km=x+k-m+1-m+1+c

Q: Sn/2 "/2 cot3 x dx

A: Given: ∫π4π2cot3xdx

Q: Solve the IVP subject to the initial conditions N (0)=1 NP N= Ntet+2 Nis the amon ht in t seconds…

A: Here, initial condition is N(0)=1

Q: terms HK K . J 12 in

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Q: En=1" Vn sin а. 1 b. 2 c. Converge

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Q: Evaluate the following integral. Sstun"s 5 tan °x dx

A: To evaluate:∫ 5tan5xdx

Q: 5 Evaluate ſ“ S" r² sin ø drdøde 0,

A: Evaluate: ∫02π∫0π∫05r2sinϕdrdϕdθ

Q: Evaluate the definite integral. S tanh x dx none of the choices O In(3) O In()

A: The functions of the form , and are trigonometric hyperbolic functions. The derivative of the…

Q: Evaluate integral S (2 sin a + 4 cos z) dæ

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Q: Evaluate the definite integral. 7 cos(t/2) dt

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Q: Evaluate the integral 3sin^2(t)cos^4(t)dt, from 0 to pi.

A: Given problem:- Evaluate the integral 3sin2(t)cos4(t)dt, from 0 to pi.

Q: Evaluate the integral. 2 [ 11t sec-'t dt 2/√√3 2 S 11t sect dt = [ 2/√√3 (Type an exact answer,…

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Q: Find Z in (1-j5) 2= tanh cos lat5 express in lagarithm Form

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Q: Evaluate the following integral 1 xp- J7+4x-5 Select one: x+3 +C 2 -1 tanh 2 -tan-1(x+2)+ C x+2 +C 3…

A: First we apply completing square method in denominator

Q: Evaluate the integral: ( ) sect tan ti +tcos 2t j+sin² 2t cos 2tk 1k)dt

A: the given integral is: ∫0π4sect tant i^ +t cos2t j^ +sin22t cos2t k^ dt we have to evaluate the…

Q: Calculate the given integral: S3 sec“(10x) dx 3) o함n a) O - tan (10x) + 3 tan(10x) + 3x + C 10 1 3…

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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.