using property of beta function prove that 57 32 S sin'x dx

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A: Given- ∫sinlnxecotxdx

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A:

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A: Given, The identity  sinx1+cosx+1+cosxsinx=2cscx We have to prove the identity.

Q: Find an equation of the tangent line at x = 0. y = x5 + cos(x) .13 (Use symbolic notation and…

A: We have given equation  y=x13+cosx Put x=0  y=0+cos(0)=1 Point on the curve x1,y1=0,1…

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Q: sin 5. Approximate | * dx| by Simpson's rule with seventh ordinates.

A: To approximate,∫0πsinxxdx    Dividing the interval 0, π into 6 equal parts each of width,h = π-06 =…

Q: (sinh x + cosh х)*3 еx

A: Solution:-

Q: 16. Using the Quotient tanx= sinx/cosx to prove d/dx tanx=sec2x

A: Quotient rule of differentiation

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A: as per the company guidelines, I can solve only one question.

Q: 4. sin2xcosx + sin x 1 xE[-27, Zn]

A:

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A: Note:- In given problem, according to written way sin2x is multiplied by 3x+1. If you want solution…

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A: The given integral is

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A:

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A: Giveny=log1+tanx1-tanx

Q: VERIFY THE IDENTITY

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Q: integral of sin2x.cos2x dx

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Q: Example 2: find ỹ,y=sin-1 Vx.sec-1 (sin x) Example 1: find ỹ,y=tan-1(x². sin x) Example 3: prove…

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Q: Differentiate the function. f(x) = sin(7 ln(x))

A: Given,         The function is fx=sin7lnx .

Q: Non Homogeneous LDE yIII  -  yII  =  3  + sin x

A: Given differential equation is y'''−y''=3+sinx. We have to find the general solution of the given…

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Q: S(sec; - sin) do

A: We know that integration power rule is  Integration of (xn) = xn+1/n+1.   Here i attached the…

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A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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Q: Use differentials to approximate the value of sin 28 degrees . Note: For ∆x, express degrees in…

A: sin 28° = 0.46977

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A: We need to find We know that

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A: Use substitution method

Q: Find the first derivative of y = (x – 1) √ (2x – x2) + arcsin (x – 1) and y = arctan [ (3 sin x) /…

A: y=(x – 1)(2x – x2)   +sin-1(x – 1) y'(x)=d(x – 1)2x – x2   +sin-1(x – 1)dx        =d(x – 1)2x – x2…

Q: Prove the identity.  cosh x - sinh x = e -x

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Q: give 3 basic derivatives examples of sum rule with solution Avoid using: cosx, sinx, tanx, logx.…

A: 1fx=x2−2xDifferentiate w.r.t "x"f'x=ddxx2−2xf'x=2x−2

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Q: DEvaluate VFano do

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: integral sin -1 x dx

A: Given Data The integral is ꭍsin-1xdx.   Let,

Q: 3 sin³ (tan √x² + 3x²)] dx d [(x²+1) cotx dx 3- cos x csc x

A: To find the following derivatives.i ddx3 sin3tan x2+3x2ii ddxx2+1 cot x3-cos x csc x

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.