sinh?x + cosh?x= ±et* %3D

Q: Find cosh 2x sinh? 2x dx.

A:

Q: (sech°x)/1+ sin? if y = dx dy Find tanh°x

A: Given:-       To find:- dy/dx

Q: cosh / 2x 18) dx Vx² sinh³ /2x

A: The given integral: This can be rewritten as, To evaluate the integral: Apply linearity the above…

Q: e sinh 2x dx

A: The given integral,       ∫e-xsinh(2x) dx

Q: sinh x dx 1+ cosh x

A:

Q: 17. sech? x tanhx dx 12

A: Integrated by substitutions

Q: Estimate sinx? dx with an error of less than 0.001.

A: Given ∫01sin(x2)dx

Q: Evaluate the integral.

A:

Q: (x?1) ore sin2x dx

A: Integrate by parts: ∫f(x)·g(x) dx = f(x)·∫g(x) dx - ∫df(x)dx·[∫g(x) dx] dx +C

Q: Find 3x? arctan x dx.

A:

Q: dx sech x (3 +5 sinh x)

A: Please see the explanation below.

Q: Find integral.

A: Given: ∫sin5x dx Now we substitute u=5x we get, ⇒du=5 dx⇒dx=15du Therefore, ⇒fx=∫sinu…

Q: By using the exponential definitions of sinh and cosh. show that cosh (t) - sinh (t)

A:

Q: sinh? 2x dx 3sinh? 2xdx

A: Given ∫-3 sinh3(2x) dx ⇒∫-3 sinh3(2x) dx⇒-3∫sinh3(2x) dx Now solving ∫sinh3(2x) dx substitute…

Q: dx х V1-4 ln?х

A:

Q: , I- Se* . sinh 2x dx

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: tanx . In(cosx) dx

A: we have to evaluate,   I=∫tanx . ln(cosx) dx

Q: Verify the identity sinh x + cosh x = ex

A: To prove the identity

Q: +4)° x = sinh4t

A:

Q: 16. 4x2 sinh (x³) tanh (x³) dx

A:

Q: Find y' if cosh x sinh?

A:

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

A: To find:∫sinhlnlnxxlnx dx

Q: y = ln° '(n*))) (tanh²(sec

A:

Q: if Pen) = Sinh(nw) find F(Z)=?

A: There is an exponential representation of sinhx. Whenever we analyse various properties of sinhx, we…

Q: Evaluate the integral.

A:

Q: Find the indefinite integral ∫sinh 6x dx

A:

Q: (3X dx =? Sinmply

A:

Q: A. Evaluate. 1 (sinhx - sinhx +coshx cosh?x 1. dx

A:

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

A:

Q: B) If sinh 0 V3 Find cosh 0, tanh 0, coth 0.

A: Given: sinhθ=32 To find: coshθ, tanhθ, cothθ. Solution: We have identity, cosh2θ-sinh2θ=1 Putting…

Q: [1+cot 2(In x2)]* dx

A:

Q: Find the indefinite integral ∫coshx/sinhx  dx

A:

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

A:

Q: /x[cosh?(2x²) – sinh²(2x²) ]dx is equal to

A: solution :let…

Q: 3. Stan tan³ 3x sec ¹ 3x dx

A: As per our company guidelines, we are supposed to answer only one question. Kindly post other…

Q: (cosh ' []] 1s dz

A:

Q: cosh?x-sinh²x = 1 %3D

A:

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: 10. S V9x2 + 64 11. ( sech?(In x) 12. S cosh(5x – 7) dx

A: Given

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

A:

Q: 4. [ x sinh x dx

A: ∫x sin(hx) dx

Q: 2. * Evsluate O 4 | dx Evoluate @ 12-X

A:

Q: S( tan + cot )2 dx. | 3 3

A: We will simplify integrant using trigonometric identities

Q: d/dx[(1-cosh(x))/(1+cosh(x))]

A:

Q: Se-Ax .sinh(2x) dx

A: We know, sinh(x)=ex-e-x2

Q: In Seln sin" x dx √√1-x

A:

Q: sech? (In x²) dx /6 tanh (In x²) – tanh² (In x²)

A: Since you have asked multiple question, As per our policy we will solve the first question for you.…

Q: Compute Jcosh'(x)sinh?(x)dx = %3D

A: We write the given integral as:…

Q: sinh(cot(x)) x2 + 1 dx

A: To Determine: find the integration Given: we have ∫sinhcot-1xx2+1dx Explanation: we have an integral…

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.