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Q: 2. cos“ y sin’ ydy

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Q: 1. -5 cosh x 2+3sinh x dx

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Determine of y = cos(x) – V5a2 In x.

A: I have stated the used formulas in the solution.

Q: |2tan x In (cos x) dx=

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Q: 2cosx dx 2 5- fn 1+(sinx)? π

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Q: 2tan x In (cos x) dx=

A: here we have to integrate the given integral.

Q: 5- = cos nx dx= [cos nx cos nx dx 0.

A: We have to solve given problem:

Q: 5z² – VE 1+ tan(x) Find an dy when y = dr Do NOT simplify. expression for

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Q: 2- X. Sin (5X) dx: Cos (SX) X Sin (SX), Cos (SX) XSin (SX) XSin (SX) Cos (SX) 25 25 25

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Q: /2 sin 2x dx Jo 3+cos (2x)

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Q: y 2sin x-cos 2.x for 0° sxs360

A: Consider the function, y=2sinx-cos2x Differentiate with respect of x,…

Q: Find for y = 5x sin x+ 10x cos x- 10 sin x. dx Dikdörtg

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Q: 3x * y^4 = 5x * sin x + 4y ^ 3 * cos x + 5y * sin x

A: Given equation is: 3xy4=5x sin x+4y3 cos x+5y sin x

Q: = (a) Evaluate S cosx sinx V1 – sin4x dx. -

A: Given∫cosxsinx1-sin4xdx

Q: Cos 2x dx ) Sin*2× + 8 1.

A: Given ∫cos2xsin22x+8dx

Q: ayfor gen f(x) = cos (2r + (/2)), a = /4 TT

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Q: Differentiate y = coS 7 + sin4x+ x cos x + 4 with respect to x. 1. 2.

A: the given function is: y=cosπ+sin-1(4x)+xcos(x)+4x3 we have to differentiate the given function with…

Q: x'+y° Q4. If u = sin- sin-'( -), Show that x+y ди X- ди + y- = 2tanx (2 + ду

A: If u=sin-1x3+y3x+y, then show that x∂u∂x+y∂u∂y=2tanx.

Q: 2 | (sin³x cos x + sinxcosx)dx 7/2 π

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Q: )if x+tany+ sin-x+ In(yx) +3**1 =4 then find y'

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Q: 3. f(x,y) tanx - sec²x - cosy

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Q: 4In(Arctan x) = 1-y

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Q: Show that bothy= sinx and y = cos x satisfy y" = -y

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: A rectangle is to be inscribed under the arch of the curve y = 4 cos (0.5x) from x = -π to x = π.…

A: Consider the given function y=4cos0.5x

Q: Evaluate the integrals

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: 2, " cos“(x)sin*(x)dx

A: To find : ∫0π2cos6xsin4xdx

Q: I3Jsin'x cos x dx .6,

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Q: Differentiate y = coS 7 + sin4x+ x cos x + 4 with respect to x. 1.

A: 1) The given equation is y=cosπ+sin-14x+xcosx+4x3 To find: dydx

Q: 2cosx dx 5- ? 2 1+(sinx)2

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Q: 8. [(cos'y- sin'y)dy

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Q: Evaluate 1- cos X dx. 2 1- cos x dx = %xp 2

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Q: aluc of 4 alue of dx. 1+(x – 2)? 1

A: See the details solution in below

Q: cos(In x) dx

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Q: 5. S sin5x cos 3x dx

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Q: 11 tanto-2 tan Bz1 show that 2 coste- Cos B20

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Q: 1-cosx 10. Find , if y = dx 1+cos x

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Q: 2. Differentiate y = /sin(x² + 3)cosx

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Q: Find dy/dx if sin-(4y²) = 8x² – 5y3 Answer: Find dy/dx if tan- (xy²) = 3x² – 5y² Answer:

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Q: 3 cos x Evaluate | dx by using substit ution method. (1+sin x)“

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Q: 5. Find the slope of the graph of cos(x + y) = 2x at the point ( 0, n/2 ). Hint: Differentiate…

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: Find 1-x if y = cos-l dx 1+x²

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Q: 4. EVALVATE | sin4x vos5x dx

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Q: Given the function y = 6 cos(3x + 1) The second derivative y" %3D Select one: 18 sin (3x + 1) -18…

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Q: Sirzy-L652X こつinてy Cos? x CoSz seczK-

A: As per guideline we have to solve the 1st one. For another solution request again

Q: S secs/2 (금x) tans (글x) dzx

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Q: 5x cos dx 2 x3 cos 9x dx X' COS

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Q: 5) ( cos 'x dx -1 Where: u = cos(x) dv = 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.