cos x sin* x dx 2. [ cor'x sin'x de 1. 7/4 7/3 3. cos x sin x dx 4. /4 | cos³x sin³ x dx

Q: x´ tanh x f (x)= tan -1 (x)%3Dtan 2 sin x+ coS X

A: This is a problem of Differential Calculus.

Q: 7. h(x) = tanx- tan 8. h(x) = 3 sec-x

A: we have been given the equations to differentiate w.r.t x

Q: 2 (sin -'x)²dx Evaluate the integral [(sin -'x) dx V1-x

A:

Q: 8. (x- cosh(sin(x – y)))= X' 9. (x- cosh(sin(x – y 10. V+coshz avôz

A: To find  The partial derivatives.

Q: 3.sin (2 4. (4 sin 3x - x) dx

A:

Q: sech (In x*) 15. dx x/6 tanh (In x2) – tanh? (In x2)

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Q: 2)/ sinh cax )x

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Q: sin 3x 22. Integrate: JS dx V25-cos² 3x A. -sin-1 (os*) + C 'cos3x' (cos 3x` C. -sin *) + C 15 B.…

A:

Q: y= sin(x + 4) cos (x - 4) y= sec 4x + tan 4x y= Arctan

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: ∫(2 cos(x) − 7sinx(x))dx   Evaluate indefinite anti-differentiation

A:

Q: integral (x 2 + 2x ) cos x dx

A: The given integral is ∫x2+2xcosx dx. It is known that ∫udv=uv-∫vdu. Let u=x2+2x   and  dv=cosxdx.…

Q: 15. sinh 2x = 2 sinh x cosh x %3D

A:

Q: (sinh x + cosh х)*3 еx

A: Solution:-

Q: 4. Interval 0<x<n, function, f(x) = sin 2x. %3D

A: We have to find the Fourier series of the function fx=sin2x ,x∈0,π

Q: 75. sin x cos x dx 76. sin 2x sin (cos 2x) dx

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

Q: This problem requires integration by parts. Find ∫(xsinx)dx sin x - x cos x   - x cos x   cos x - x…

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Q: cOs x 1. S sin x (1 + cos x) ecosx dx

A:

Q: cOS X COsy dx + (1- sin x siny) dy of from X = 0 the urrve y sihx

A:

Q: cos3 3x dx Vsin 3x

A: We have to solve integral.

Q: cosh x sinh x dx 2 (cosh x + 3)

A:

Q: sin x dx 1- sin2 x 4. cos x dx 2+3 sin x 5.

A:

Q: 7. y= (x²-1) sinh (x+1)ª 8. y= sech (1-x³) 9. y =- tanhx

A: Answer (7): The given function is y=x2-1sinhx+14 using product rule in differentiating above…

Q: 2 (sin x cos x + x) + C - 2 (sin x cos x + x) + C (sin x cos x + x) + C -(sin x cos x + x) + C [(cos…

A:

Q: SV1+ sin2(x - 2). sin (x – 2). cos (x – 2) dx

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: x*sin (2x) dx a. ** cos(2x) – x³ sin(2x) –r² co. 3 x² cos(2x) +x sin(2x) +- cos(2x) + C 4 1 cos(2x)…

A:

Q: Intergal of (sinh x) / (cosh x + 6) dx

A: To find  Integration of (sinh x) / (cosh x + 6) dx

Q: 12. Find the first derivative of y = 2cos(2 + x*). A. -4x sin (2 + x2) B. 4x cos (2 + x*) C. x sin…

A: Questiopn no. 12,Given,           y=2cos2+x2To find : The first derivative of the function.

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…

Q: eCoS ecos x sin x dx In x 2. Vx 3. tan'x dx

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Q: sin 2x+sin x dx Vsin2x -cos x v.

A:

Q: cos*(x)dx

A: According to integration reduction formula ∫cosn(x) dx=n-1n∫cosn-2(x) dx+cosn-1(x) sin (x)n . For…

Q: ✓cos x lim x 0 1 cos x - -

A: The given limit is limx→01-cosx1-cosx

Q: (sin x + cos x)dx sin² x sin 2x sec x dx sin 2x dx 2 sin x cos² x

A:

Q: ∫ cos (ln(x)) dx

A: Given-∫cos(ln(x))dx =∫xcos(ln x).1xdxLet u =x      and      dv= cos( ln x )1xdx  So,du=dx      and…

Q: )Find the anti derivative for sin(x^2) 2x

A: we have to find the anti derivative of ∫sinx22xdx...............1 first we put in place of x2 =z…

Q: 1. DERIVATIVE OF TRIGONOMETRIC AND INVERSE TRIGONOMETRIC FUNCTIONS. Find dy/dx, 1. y = sin (x + 3x +…

A: d/dx(sinx)=cosx d/dx(xn)=nxn-1 d/dx(cosx)=-sinx

Q: e*+ cos x (d) h(x) = tan x (e) y = Vx sec x e* =dx.secX.さャx.d secxrが4リxのsecX.àビ…

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Q: 3 sinx+cos x Evaluate S dx. 2 sinxcos x

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Q: ∫ sin3 (x / 2) cos (x / 4) dx

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Q: 3 √√√x tan-¹ √x dx 1. 1 2. T 3. 3x² + 4x³ +16x² +20x+9 (x+2)(x²+3)² 1 12x+5x+3 4. 0 √ sec¹ x tan³x…

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Q: Integral of sin^4 (x/2) cos^2 (x/2 dx

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Q: sin x dy (1 + y) cos x + sin x If y=- , prove dx %3| cos x 1+2y + cos x- sin x 1+ sin x 1+ 1+ coS x…

A: Introduction :

Q: ( (cos (2x) – sin(2x) cos( 2x)) cos (x) – sin(x) For (x) +C. What is F (x)?

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Q: V1+ sin (x5) e-y 2(Vx- 1) f-- cos {sin(2x*)} x-2 x2+3x

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Q: Solve over the interval [0,2pi)

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Q: ∫(3 cos(x) − 7sinx(x))dx   Evaluate indefinite anti-differentiation

A:

Q: sinh (2.Inx) n(coshx+Sinhx)+in(cashx-sinh x).

A: We have to rewrite the given expression by using the exponents.

Q: cos(2x)- sin(2x)cos(2x)) cos(x)- sin(x) dx = -F(x) + For C. What is F (x)? 3.

A:

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.