Write 9 sinh(x) + 4 cosh(x) in terms of e and eX.

Q: Derive the formula sinh-1 x = ln (x + sqrt(x2 + 1)) for all real x. Explain in your derivation why…

A: Define y as follows.

Q: | sinh$4x cosh 4x dx can best be evaluated by General Power Formula. A True B False

A: Explanation of the answer is as follows

Q: 101 Jzy cosu(x) + sinh(x)

A: Given differential equation:d2ydx2-y=coshx+sinhxTo find: General solution. Note:1 coshx=ex+e-x22…

Q: sinhx dx 1+ coshx ) A 1+ coshx B (1+coshx)? (1+coshx)² D 1+ coshx

A: We have to find

Q: Write sinh(x) + 4 cosh(x) in terms of e and e

A: Given: 9sinhx+4coshx   -1 The objective is to write 9sinhx+4coshx in terms of ex and e-x. Since,…

Q: t2(sinh 2.75t – 5)

A: (3) Given t2sinh2.75t−5 We have to find the Laplace transform of t2sinh2.75t−5 That is…

Q: Sin * :-

A: Solve the integral by using substitution method . Basic integral :∫xndx = xn+1n+1

Q: tan25x dx 4sin25x-4

A: Simplify the integral ∫tan125x dx4sin25x-4 using the trigonometric formulas (1-sin2x)=cos2x and…

Q: S sin°xcsc³xdx

A:

Q: In each part, rewrite the expression as a ratio of polynomials. (a) cosh (ln x) (b) sinh (ln x) (c)…

A: a)  Given expression is cosh ln x. As cosh x=ex+e-x2 So, cosh ln x=elnx+e-lnx2=elnx+elnx-12=x+1x2…

Q: Differentiate.   y = In (Cosh 3x)

A:

Q: 1- Y= sin( coshx log, 2 )

A: Given: 1-y=sincoshx log22

Q: 2 Cosh2x- sinh2x A

A: Given, 2 cosh 2x - sinh 2x =2              (1) We know that,           cosh x =ex+e-x2sinh x…

Q: sinh5x S sinh*xcoshx dx is a)True b)False

A: This is true.

Q: +4)° x = sinh4t

A:

Q: Write ∫ tan2k+1 x dx, where k is a positive integer, in terms of ∫ tan2k−1 x dx.

A: Given integral is ∫tan2k+1dx. Rewrite the above integral as follow.…

Q: In the given question, verify the identity:- cosh x - sinh x =- e-x

A: As we know that the hyperbolic function of the inverse trigonometric identity is given by as…

Q: Write 6 sinh(x) + 3 cosh(x) in terms of ex and e−x.

A: here given that 6 sinh(x) + 3 cosh(x) the value of sinh(x) and cosh(x) are.. sinh(x) = ex/2 - e−x/2…

Q: In the given question, verify the identity:-   sinh 2x = 2 sinh x cosh x

A: To prove  sinh2x=2sinhxcoshx.

Q: Simplify the equation: sechx + sinhx tanhx cosh z cosh a sechx 1+ sinh 2 cosh z

A:

Q: Evaluate L, sinh 3t (3

A: L13sinh3tUse the constant multiplication property of Laplace Transform:For function ft and constant…

Q: In(ere + 12) dx Xet

A: Given : ∫x2ex2lnex2+ 12dx

Q: Write 9 sinh(x) X. + 6 cosh(x) in terms of e* and e + le-x

A:

Q: Use Integration by Substitution to find sin(x²) 2x dx

A: As per our guidelines we are supposed to answer only 1 question. Please repost other questions as…

Q: 8) Find the dexivative of fex) - sinx cos x, Write your answer Single term. as a

A:

Q: Differentiate sin(3x+5) with respect to x

A:

Q: Write sinh(3 ln(x)) as a rational function of x.

A:

Q: Find the Indefinite Integral. Sinx cossx xp-

A:

Q: Solve dy *- Jxy +1 with yeo) =1 for finding yfo.075) dx take h=0-025

A: The numerical solution of the differential equation is the value of the function that satisfies the…

Q: Evaluate ∫ 3x2 sin(x3) dx.

A: To evaluate the integral  ∫3x2 sinx3 dx

Q: -1 Cosh-1 5x sinh 4x.

A:

Q: – 3r) sinh 2r.dr))

A: We will find out the required value.

Q: Evaluate : e2x sin3x dx

A: Introduction :

Q: Derive the formula sinh-1 x = ln {x + √(x2 + 12)} for all real x. Explain in your derivation why the…

A: Consider the formula as:                         Let:                                   y=sinh-1(x)…

Q: solve cosh2x= tanh!

A: The equation is solved as shown below

Q: Evaluate: (cosh22r+ sinh²2r) dr

A: Our Aim is to evaluate the integral given below:-∫cosh22r+sinh22r-(i)

Q: Find the antiderivative of sin(square root of 5x)

A: Consider the given function:

Q: what is -sinh(x) equal when x = 0

A: We know that   sinh(x)=ex-e-x2 Then -sinh(x)=-ex-e-x2 now substituting x=0 in the above equation…

Q: Write the expression as an algebraic expression in x for x > 0.

A: Given: secsin−1xx2+4

Q: #1. ( sin2r #2. rp- sinz 13. L #4.

A: To solve the given integrals we must know about the power rule of integration and trigonometric…

Q: Write sinh(7 ln(x)) as a rational function of x.

A: Given sin h (7 ln x)

Q: Sketch and Evaluate 27 sin 77x² - dx dy x2 Jo

A: consider the equation

Q: Derive the formula Cosh x

A:

Q: Please determine Į In(x2 + 1) dx.

A: The objective is to evaluate the integral.

Q: find the implicit formula of sinxy=x+y

A: Given,

Q: Solve 0's X <360 for x, Such. that 7sinx 8. Sinx 10 ナ

A:

Q: dx 9. JI+Vx+1

A: To evaluate the given definite integral.

Q: how that 1 dn v2

A:

Q: Evaluate 12 xsin'x dx V1-x?

A:

Q: dx 8) x*Vx² +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.