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

Q: Find derivative of the following functions 1. y= sin^-1 2x^2 2. y= tan^-1 2x^2/5

A: Given 1. y=sin-1(2x2)2. y=tan-1(2x25)

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: 22. Evaluate S tanºx sec² x dx

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Q: Integrate cos2x/sin^2(2x+8) dx

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Q: Integrate: S tan (æ) sec³(x)dx

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Q: Evaulate the intergral: ∫−10sec^2(x)tan(x)dx

A: Consider the given integral:

Q: 1) Find 4 by implicit differentiation given 4 cos x sin y = 1. dx

A: Differentiate above equation with respect to x.

Q: x – sin 2x -dx x + cos2x

A:

Q: integral of sin^5(3x)cos^3(3x)dx

A: The integral of ∫sin5(3x) cos3(3x) dx is sin5(3x) cos3(3x). If we need to find the integration then…

Q: 4. X sin (x) dx VI-X 1-メ-

A: “Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Find. S sin3 2x cos3 2x dx

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Q: = In(x² + y- sin sin-1 a2.. ||

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

A: Given∫cosxsinx1-sin4xdx

Q: Find the derivatives of the functions in Exercis

A: Chain Rule: f(g(x))'=f'(g(x))g'(x) Differentiation formulae: ddxsinx=cosxddxcosx=-sinxddxax=a

Q: Cos 2x dx ) Sin*2× + 8 1.

A: Given ∫cos2xsin22x+8dx

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: 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: Find /e2x sin(2x)dx

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Q: find integral sin 5 x  cos 2  x dx

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Q: Evaluate. S sin“ x cos² x dx

A: This question is related to integration,  we will solve it using given information.

Q: 1. S cos (3 sin x)cos (4 sin x). cosxdx sec*x dx 2. Jtanx 3. Sr 6 tan*x dx 4. /2 sin5x dx

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Q: 2, " cos“(x)sin*(x)dx

A: To find : ∫0π2cos6xsin4xdx

Q: Compute sin x dx er + 3e -x 8.

A: We have to compute the given expression ∫sinxex+3e-xdx from -∞ to ∞ Therefore, The  given expression…

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: 1. Find , if y = x² sin 3x dx

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Q: 6. Find [sinh(4x)sin(2x)dx

A: By using integration by part.

Q: S sin(4 + 5x) cos (5x – 4)dx

A: From the given problem: I=∫sin4+5xcos5x-4dx As we know that the trigonometric identity:…

Q: 9. tan 4x sec24xdx d. cos 5xsin 5xdx e. x sin(3x² +1)dx f. [x* cos(2x' +1)dx

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Q: Find cosh æ In(sinh x)dx.

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Q: S sin (3x) 1+cos² (3x) dx

A: Given integral ∫sin(3x)1+cos2(3x)dx The objective is to evaluate the integral.

Q: Find* esin ¤ dx tan x csc x cos x e $in xt. - cos x e Sin x + c Option 4 Option 2 esinx + c ,sin.…

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Q: Find cos x + sin 2x dx 19. sin x

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Q: 4. sin 2x cos 2x dx

A: Here we integrate the given function.

Q: 16. S sin 3x cos 3x(cos 3x+1)² dx

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Q: Find y' by implicit differentiation: 8 cos(ry) + x4 = yª

A: Given: 8cosxy+x4=y4 For finding derivative of given expression, we differentiate given expression…

Q: 4. Use implicit differentiation to find az in xexyz sin(2z) – xyz = 5. ду

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: cos(In x) dx

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Q: Evaluate sin (4x) cos -2(4x) dx. | sin (4x) cos -2(4x) dx = O

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Q: Va2-x² Y=Arc sin- + а

A: Solution-

Q: Sõ sin“ 3x cos 3x 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: 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: Integrate: S dx sin ³x cos6x

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Q: E PARTICULAR SOLUTION OF EVERY EQUATION GIVEN. [tan y – (In x)°]dx = 0 When:x = 1; y = " 4

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

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Q: S secs/2 (금x) tans (글x) dzx

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Q: S sin 3x cos xdx

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Q: dz 5 – 2x cos 2x dx 1 + sin 2x sec² 0 de. tan 0

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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.