2. y = Ce*cosx + C2e*sinx

Q: Explain how to find ∫ cos15 x dx without actually integrating.

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Q: par y) В. х2 + у2 С. sin (3x — у)

A: Which of the following equations are solutions to the partial differential equation

Q: If y=sin(sinx) show that y'' +(tanx) y''+y cos2x=0

A: we have to derivate 2 times then we will get result

Q: 11. y = sin 12. y = cos*(-) 13. y = arccos(-) %3D 14. y = arcsin (- 5

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Q: 4. Verify. COSX 1+sinx = 2secx %D а. 1+sinx COSX b. cosx(1+ tanx)² = secx + 2sinx %3D

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Q: 12.y = sin(tanx) 13.y = 2sinxcosx cosx 14.y = x2 tanx 15.y = sinx

A: We have to find derivative

Q: 5. y = tan- (a) 6. y = 4x sin (3x - 9) 7. y = sinh (4x – 1)

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Q: If y=sin 2x sin 3x sin 4x then find y''

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Q: 2. tan3x(sec3x – cos3x) dx

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Q: 38. Differentiate y = 2 cos² - a. – sint b. - sin 2t C. - sin - d. sin-

A: Differentiate y=2cos2t2

Q: 15. cos³ 3x 3√√/sin 3x dx

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Q: If y=sin(sinx) show that y''+(tan x) y'cos2x=0

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Q: Differentiate y=(1-cosx)/sin2x

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Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x %3D

A: NOTE:according to company rules I need to solve first question when multiple questions are posted

Q: 4. y = tan¬1(3x) cos 1 4x 5. y =

A: To determine the derivative of given functions. Here we will use the following formulas-…

Q: 4. sin Tx - y = 0 4 -- y = -1 5.

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

A: Given∫cosxsinx1-sin4xdx

Q: 5. Find y', if y 2cosx sin2x – sinx cos2x %3D

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Q: Differentiate y = (1+ sin* (æ²)) °. 3 8.

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Q: Differentiate y=(sinx)2(sin-1x)2

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Q: f y=sin(sinx) show that y'' +(tanx) y''+y cos2x=

A: Given that y=sinsinx To show that y''+tanxy'+ycos2x=0

Q: 4, 8 sec3x tan5x dx

A:

Q: 2, " cos“(x)sin*(x)dx

A: To find : ∫0π2cos6xsin4xdx

Q: 4)Lin sinx %3D メ→ x3 ート。

A:

Q: 1- Differentiate. a- Y= 2 ex¹2-1 b- Y= -2 sin³x c- Y= 3sin2x - cos 4x d- tan√(1-x)

A: solution:-(a)  y=2ex2+1dydx=ddx2ex2+1       =2ex2+1ddxx2+1,    chain rule      =2ex2+12x…

Q: 5. | sin (Tx) cos (Tx) dx

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Q: 1-Sinx finel y 14 Sinx

A: Consider the given function, y=1-sinx1+sinx use the quotient rule of the differentiation which…

Q: I3Jsin'x cos x dx .6,

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Q: If y = sin 2x sin 3x sin 4x then find y".

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Q: 23. cos (3z + 4) dz 25. sec2 (3x + 2) dx

A: A

Q: [17 sin³ x costx dx 5.

A: Given: I=∫17sin3xcos4x dx. To evaluate: Value of integral I.

Q: 2 , 1 + sinx +. D. cosx cosx il + sin.x

A:

Q: ∫cos(15x)cos(4x)dx

A: Integration and differentiation can be considered as inverses of each other. Integration is mainly…

Q: 4. Y" + y = 2x sinx

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Q: 16. S sin 3x cos 3x(cos 3x+1)² dx

A:

Q: Number 17

A: First we break sin^3 x in sin^2x*sin x, and then we replace sin^2 x by 1-cos^2 x.THen in the next…

Q: 1. sin (3z) cos5(3z)dz

A: Note -  Acc. to Bartleby guidelines, we are supposed to do only one question . If you want more to…

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: = 2. If y = sin³ (-) cos³ (1) prove that y' = sin² (x) cos(x)

A: Topic = Derivative

Q: 1. y=1+sinx 2. y=(1/6)cosx 3. y=cosx+2

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Q: 2. S CoSx+sinx-1

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Q: 2 2- Find if y = dx sin2x sinx

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Q: 5- y = 1+sin(4x2 + 2)

A: Note - As per our guidelines we will solve first question only and rest will reposted.  ddxxn =nxn-1…

Q: If sinx = siny = a and cosx = cosy = b,then cos(x-y) is

A:

Q: 04.) Show that y = (sin x +cos x) sec x = sec² x

A: Given inequality does not equal. See the attachment

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.