hD (Hint: E =eD and Sinh x: 2 Q3: Prove that 8 = 2Sinh %3D

Q: 9. t² cosh 3t 10. t³ sinh t

A: solution of the given problem is below using laplace transformation...

Q: Separate tanh-1(x+ iy) into real and imaginary parts.

A:

Q: Find the value df (a) that Make ECX) is Contincity at X- Ž

A: Given that :f(x)=cosx2x-π      ,             x≠012a2-3a+4      ,   x=0

Q: d dx A.sinh(Inx) B.–sinh(Inx) sinh(Inx) C.- X -cosh(x) D. X cosh (Inx) =

A:

Q: Latel I, Vx2 + y² dV,

A: answer is in next step

Q: (8) dx Compared to I dx x In|x| Conterges or Diverges

A:

Q: test for the exactness of the differentral dy + Cosx +Sinyfy -0 quation And hence find the Salution…

A: A differential equation contains independent variables, dependent variables, and the differential…

Q: Evaluate dx dy in y=cosh(in e") b. 3x sinh (In x') 3x² sinh(In e* ) d. 3x sinh (3x² ) с. a. 3x…

A: Given:     y = cosh ( ln ex^3 )

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

A:

Q: f(x)% 3D tanh In(2x) is equivalent to

A:

Q: dx х V1-4 ln?х

A:

Q: b,c,d

A:

Q: 9. Vy + dy 415

A: We will be using the given rules to evaluate the answer

Q: Hiw proo p. s (sinh at) =_a s- at Notes at

A: Explained below

Q: 2*csch( 2*) d x cosh(2*)-sinh(2*)

A:

Q: Verify the integration formula. S 6 sechx dx = tan-1 (sinh 6x) + C (A) No B) Yes

A:

Q: dy log x If xY = ex-Y, prove that %3D dx (1+ logx)?

A: Introduction :

Q: e dx 1- e2x (integration by substiution)

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

Q: 6.) y'of y = Insin(arctan 3x)

A: This is a basic differentiation question

Q: sinh(In In a)da is equal to xlnx

A: To find:∫sinhlnlnxxlnx dx

Q: Q3: Let cosh(x)3D5, x>0 , Find values of: sinh(x), tanh(x).coth x ,sech x,csch x

A: Given, cosh(x)=5, x>0

Q: L{e _at sinh(-at)} s2+2as - (s-a)" (s+a)?

A: Given L{e-a tsinh(-at)}

Q: Question The approximation of fxln (x + 5) dx using two points Gaussian quadrature formula is:

A:

Q: Use Romberg's method to compute dx 1+x? correct to 4 decimal places by taking h= 0.5,0.25 and 0.125.

A: AS PER OUR GUIDELINE WE ARE SUPPOSED TO ANSWER ONLY ONE QUESTION. KINDLY REPOST OTHER QUESTION AS…

Q: zy (Smxa CosX) Axー Sinhy

A:

Q: 3. Arctany dy

A:

Q: (log a) dx 1+x²

A:

Q: S tan ax secex dx 3

A:

Q: The Smith's invest $10,000 in an account that grows to $12,000 in 5 years. What is the annual…

A: Consider the given smith invest $10,000 in an account that grows to $12000 in 5 years

Q: I) Find the volume of the solid obtained by rotating the sine function between x -0 and x x about…

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Q: hat is the number equal to L sin (3rt) dt?

A:

Q: d 55. Vcosh x +1 (cosh x + 1)-/2 sinh x dx

A: Given The function is f(x)=cosh x +1 .

Q: ex/Eveiluene the fallowing integrels 21/dx XInx

A: The given integrals are 1. ∫dxx1-x2. ∫dxx ln x

Q: Differentiate y= 3-carhx tespect to X 6+ Sinh x

A:

Q: Use Gaussian Quadrature of order 5 to approximate 08 6 2 x-1 To how many decimal places is this…

A: Given that,    f(x)=∫286x-1dx                                  1 Using the Numerical Integral by…

Q: Jrin m In(cos m) dm

A:

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

A:

Q: From the figure formed in integrating -dx, what is the term or value that is adjacent to the angle…

A: Given:    ∫x2-3xdx

Q: Find the length of y = ln (sec x) between x = 0 to x = π/4.

A: you meant to find the arc length of y=ln(secx). the formula for the length of the arc in the given…

Q: d y' of y= In(tanh2

A:

Q: (f) y = e* In(tanh(x))

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Q: ich option is an antiderivative of Sar 3x cos(-2x) dx a. 3 9.

A: We will use integration by parts to find the answer.

Q: Using integration, derive the La L(sinh at)

A:

Q: 1:10 PM Wed Nov 24 Inverse hy perbolio AUTIVITY Oy = sinh (2x+-1) cosh Sza ☺ y= tanhB | -| /2

A: We have to find the derivative

Q: d21 0 is sinh(a) dx21 at x = 0 is

A:

Q: a. Find the root mean square value of tanh x, for 0 < x< 2.

A: we know the formula of root mean square, rms = [ (1/b-a) (integration of |f(x)|2 from a to b) ](1/2)…

Q: Find y' of y= In(tanh2x)

A:

Q: Calculate the exact value of the intergral ∫ln(x)dx where b = 3 and a = 1

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.