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

Q: Find the indefinite integral ∫sin 5x sin 4x dx

A:

Q: By using the definition of hyperbolic functions as exponential functions, show that sinh 3x = 3 sinh…

A: handwriting solution

Q: Derive the following function 8. y = tanh-1(sinx)

A: We have to find  the derivative

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

A:

Q: Evaluate the indefinite integral. sin(-3x) dx +C.

A:

Q: Use Newton Raphson methods to solve X |sin(x)| = 4.1

A: Newton Raphson method: Roots of the equation f(x)=0 are given by iterative formula…

Q: Find the indefinite integral. sinh(6 – 7x) dx

A: Consider the integral  ∫sinh(6-7x)dx

Q: e sinh 2x dx

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

Q: Find the indefinite integral.

A: According to power rule of integration .

Q: Integrate the square root of (1 - sin² x) dx.

A:

Q: Find the indefinite integral. ∫ sinh x/(1 + sinh2 x) dx

A:

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

A:

Q: A ( sinh x- coshx tanh e 6)

A: You all need to have the idea of hyperbolic and their basic calculus.

Q: evaluate the definite integral from [0,pi] [(sinx)2(cosx)4]

A: To integrate the definite integral

Q: evaluate the definite integral of " sin^2{x} " from [-pi, pi]

A: We will use the reduction formula to solve given definite integral

Q: +4)° x = sinh4t

A:

Q: Find y' if cosh x sinh?

A:

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: Find the indefinite integral. sinh(4 - 7x) dx

A: evaluate the indefinite integral ∫sinh4-7xdx

Q: 4. f(x) = -sin Зл PS = DCP 11 VS =

A: We have to find the amplitude, phase shift, vertical shift and period of the given function.…

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

A: To prove  sinh2x=2sinhxcoshx.

Q: Evaluate the indefinite integral. ∫sin5(x)cos4(x)dx

A: Integrate the given indefinite integral as follows.Consider the expression sin5(x)cos4(x).The above…

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

A: To find:∫sinhlnlnxxlnx dx

Q: sinh 3x –1 H(x)=: 1+cosh 3x –1

A: Given: H(x)=sinh3x-11+cosh3x-1 To solve: The given function.

Q: sin 3x• tan 3x

A: Given integral,

Q: 2- Solve the equation for x : Cosh x = Sinh x +1/2.

A: We need to find out the value of x. The given equation is Cosh x=Sinh x+12 Now,  Cosh x=ex+e-x2  and…

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

A:

Q: 3+ cos(log, x) xp- x sin?(log, x)

A: Given I=∫3+cos(log4x)x sin2(log4x)dx Let assume log4x=t ⇒1x ln 4dx=dt⇒dxx=ln 4 dt

Q: Evaluate the integral.

A:

Q: Find the indefinite integral  ∫sin3 3x dx

A: Given: ∫sin33xdx

Q: Find the indefinite integral. sinh(8 – 7x) dx

A: From the given problem: I=∫sinh8-7xdx  ....(1) As we know that; ∫sinhxdx=coshx+C

Q: Evaluate the indefinite integral. sin°(13x) cos“(13x)dx

A:

Q: Find the indefinite integral ∫sin 4x dx

A: We know that,  ∫sintdt=-cost+C           ⋯⋯1 We have the given integral as I=∫sin4xdx

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

A:

Q: Find the indefinite integral ∫sinh(1 − 2x) dx

A:

Q: Find the indefinite integral. sinh(4- 5x) dx

A: To find:∫sinh4-5xdx

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

A: solution :let…

Q: Q3: Find value of x if 3 cosh x- sinh x= 4

A:

Q: cosh?x-sinh²x = 1 %3D

A:

Q: ecot ha dx sinh x cosh x + e sinh2 x

A: In this question, we need to evaluate the given integral.

Q: cosh(2x) = cosh?(x) + sinh² (x).

A:

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

A:

Q: If f(x) = sinh 2x − e2, find the exact numerical value of f"(ln 2).

A: Given : f(x) = sinh 2x − e2

Q: Evaluate the integral.

A: ∫cosh2(x)sinh(x)dx

Q: 1- y '(2x) = Sinh

A: the question is taken from calculus and in which we have to find the derivative of the given…

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

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

Q: Explain how to find ∫ tan15 x dx without actually integrating.

A: ∫tan15x dx=∫tan13x tan2x dx=∫tan13x sec2x-1 dx   ∵sec2x-tan2x=1=∫tan13x sec2x-tan13x dx=∫tan13x…

Q: As x gets closer to zero, tan2x/ln(1+x) gets closer to what value?

A: This question can be solved using the concept of L HOSPITAL,'S RULE.

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

A: Given,

Q: Find the indefinite integral. sinh(2 – 9x) dx

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.