Se Sin (3x) dx by Improper htegrations.

Q: Find dy/dx by implicit differentiation. (cos TX + sin Ty) = 18

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Q: find dy / dx by implicit differentiation.

A: In implicit differentiation, on differentiating y, we use dy/dx.

Q: Find the intergration of x^3(x^4-sine)^5 dx

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Q: 35. tes ушх хе" dy dx 0,

A: Given the integral:

Q: If y = (2x)sin (4z) , then dy sin(4æ) · (2sin(4z) esin(4z) In(x)) %3D dx X synta

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Q: Integrate O sinh 2x dx

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Q: 3) y sin-ly² dy

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Q: Evaluate cos √6x dx using a substitution followed by integration by parts.

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Q: Find dy/dx  if  4 cosx siny = 1

A: We will directly differentiate it.

Q: If y=(sin3x-cos3x)², find dy dx

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Q: ind dy/dx of y= tan^-1 (ln x^2

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Q: (d) y = sin(Vx) sinh (In x)

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Q: L(cos(at)sinh(at))

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Q: Differentiate implicitly to find dx Зху + 5 3 0 dy %3D dx

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Q: Find dy/dx, where xsiny +ysinx=1.

A: Given - xsiny+ysinx=1 To find dydx Here we will use the following formulas- ddx(uv)=udvdx+vdudx…

Q: 23. Lx? sin y dy dx

A: Given: ∫-11∫0πx2sinydydx for finding given integral we integrate one by one

Q: sinh (:) dz dy dx

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

A: To find:∫sinhlnlnxxlnx dx

Q: find dy / dx by implicit differentiation.

A: Given equation is x4y-8xy+3xy2=9. To find dydx. Solution: Power rule of differentiation states that:…

Q: find dy / dx by implicit differentiation.

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Q: Find dy if y = tanh-1(5x²) csch¬'(In x). dx

A: Given: y=tanh-1(5x2)csch-1(lnx)To find:dydx=

Q: arctanx e dx (1+x²,"

A: The given problem is to evaluate the given integral. We have to evaluate by using substitution…

Q: dy Find by implicit differentiation. 20x = 20 - ey ... dx (Type an exact answer.)

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Q: y= sinh(2n)-글교 dy/dx gi

A: Derivative of sinx is cosx.

Q: Evaluate xy dy dx ?

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Q: Evaluate sin(x) · In ( cos(x)) dx using integration by parts.

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Q: find dy / dx for Hhe tellowing in (sec EX) In (cosp?}

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Q: Integrate: / cos“ x dx

A: The given integral is: I=∫cos4x dx Reduction formula: ∫cosnx dx=1ncosn-1(x) sin(x)+n-1n∫cosn-2(x) dx

Q: find dy / dx by implicit differentiation.

A: Implicit differentiation is performed when the dependent variable cannot be explicitly written as a…

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: If y- sinhx then prove that dy dx

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Q: find dy/dx if(cosx)y=(siny)x

A: Given: -

Q: (a) --y = 2x?y, y(1) = 1 dy dx

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Q: If y = (sin-' x)², show that (1 – 2*) dy dr? dy 2. dx

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Q: lel sin(mx) sin(nx)dx=0 (a)

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: dy Find by implicit differentiation. dx 14 In x= 18 - In y dy dx (Type an exact answer.)

A: Consider the given expression 14ln x=18-ln y.

Q: dy of y = sin(3x² + 5x – 4) * In(e*) is dx

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Q: Change the order of in tegration 10 10 dy dx

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Q: Integrate: cos Gx) – sinh(2x)]g

A: As per our guidelines only one question can be answered.Please repost the next part in next…

Q: dy/dx of y=5^cos(3x+5)

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Q: Find dy/dx by implicit differentiation. (sin mx + cos my)4 = 74 dy/dx=

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Q: Show that ∫∞−∞ sin x dx diverges.

A: To Show: ∫-∞∞sinxdx diverges.

Q: Differentiate. y=de* +6 dx

A: Given y=ex+6

Q: find dy / dx for Hhe follo wing 2X y=3+ ln (sin x?)+In (sin 5x)

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Q: y = In(x +1)

A: Given that : y = ln(x2 + 1). Find dy/dx  We know that derivative of - d(lnx)/dx = 1/x. And d(xn)/dx=…

Q: Integrate x?dx

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Q: dy dx sin( y)

A: Given: The differential equation is x 2 y ' = sin(y) .

Q: 1 B3. Evaluate dx, using substitution method.

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Q: = Evaluate Se cos 3x dx using integration by parts method.

A: Given,          ∫e-3xcos3xdx

Q: Cualuate the definle integial. x33 COs (xH) dx

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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.