8. y"+y = 3 cos 2.xr,

Q: 3(sin y- cos y)* dy cos y

A: We need to solve the integral ∫3sin y-cos y2cos ydy Now, we have an identity a-b2=a2+b2-2ab Hence,…

Q: Suppose that y = 4 cos² t , x = v3 sin(2t) and 0 < t<a. Then dt2

A:

Q: 4. Show that sin(0 – ø) R2 – 2r R cos(0 – 4) + r² dø = 0. -

A:

Q: 2.1 Given that sinh x = [e" – e=*] - - show that dy cosh a. da

A: To Determine: show that dydx=cosh x Given: we have sinhx=12ex-e-x Explanation: we have…

Q: Find dy/dx for y = (cos x) 2 + sin(x 2 )

A: Given that      y = (cos x)2 + sin(x2) We have to find dy/dx .

Q: 5. S 11 sin ( 4x – 6y) cos ( 6x – 4y) dy - -

A:

Q: 2FI 2 sin nx dx cos nx dx =0, where n integer. %3D !! 0.

A: Note: -     as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 1 1 S [ sin(1+ y²)dydx= 1- cosl a. 2 cos 5

A:

Q: of cos 2 2 sin 0) de has the form 1 -F 4 sin lue of 0 to make F(0) =0?

A:

Q: 4. Find fyryzyaz, if f(r, y) = x² cos[100(e" + /1+ y²)®]

A: Given; f(x,y) = x2cos[100(ey+√(1+y2))y]

Q: 3) еУsinx dx %— cos²x dy

A: Differential equation

Q: tan x dy +y sin x dr = 0, when x = 0, y = | O y (3- cos 21) = 2 O y (cos 2x O y° (2 – cos 2x) = 1…

A:

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

A: Given  y = (1- cosx) /(1 +cosx) To find dy/dx

Q: 9. Integrate: Ja (x- 1) cos(x? - 2x) dx

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 8 Find L-- 8s2+6 sin Vt cos Vt COS V V등 sin y응t COS

A:

Q: 9. If y = costhen the second derivative is 5x 25 Cos, 16 5x 5x sin- 4 d. 25 5x sin- 4 a. 25 b. C -25…

A:

Q: Show that L{cos at} = S s² + a² Hence find L{sin 8t sin 6t}.

A:

Q: dr 1- y = Inlog 2- y = (cos x)*Snx 3- у e (sinx

A:

Q: dy Cos(3x) + (In x)

A:

Q: 1od of undc cients, obtain the general y" – 2y' – 3y = 2 sinx

A:

Q: (b) Show that 2t cos x and sin x = 1 + ? (c) Show that dt dx 1 +

A:

Q: 2. if 2x3 +10 x?siny-y"tanx = 0 ノ the y' so dy write ex pressin in terms of X and y.

A: Applying implicit derivative we have

Q: Differentiate: y = In cosh (cos 2) O y' = 6 sin 2z tanh(cos 2z) y' = -6 sin 2a coth(cos 2x) Oy = -6…

A:

Q: 3) Show how the substitution u = 2 x shows that - - t/2 -Tt/2 S sin"x dx = S? cos"x dx

A: Let u=π2-x Differentiating u w.r.t. x- dudx=-1du=-dx Considering left hand side of the given…

Q: 10. Given that 2y- sin 2x =0 and y = 0 when x 0, then y?= %3D %3D dx B. 1-cos 2x C.-2 cos 2x A.…

A:

Q: V3 with 0 < x < 2n. 2 cos 2x cos x – sin 2x sin x - -

A:

Q: 2- Find of y = dy dx y %3D /cos-1(In (xy))

A:

Q: i) L-- (In) L- | s-3 6s+3 ii) L-1 iii) L(tet cos wt) s+1 sª+5s2+4,

A:

Q: 4. y = tan(x+ a), 5. y = Aex + Be2x, 6. y = A sin 3x + B cos 3x, ,where A and B are arbitrary…

A: According to bartleby guidelines when student ask multiple subpart question then expert must have to…

Q: ( cos nx dx= [cos %3D nx cos nx dx 0. %D

A: We have to find the integral of cos2nx dx from 0 to 2pi.

Q: 18) * x-sin 2x ; find y" y y" cos 2x y = 7 %3D Option 3 O Option 1 y" sin 2x

A: First we find out first derivative with respect to x then we find out 2nd derivative with respect to…

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

A:

Q: (2) Show that y=x sinx is a solution to y"+y= 2 cos x.

A: To Show: y=x sinx is a solution to y''+y=2cosx

Q: 3. In (cose) tane de

A:

Q: 4 sin' 2x cos 4x dx 4.

A:

Q: 7)(x+tan y) dy sin 2y dx

A:

Q: A particles velocity is 7 cos(2t) meters per second. at time t=0 its gone  2meters, where is it  at…

A: The velocity of the function is given as:

Q: y"+4y=sin 2x, where y(0)=3 and y'(0)=¾

A:

Q: 1- LS7 cos(y)esin(y)+9x dydx 2

A:

Q: +15 - If y = cos-1(x) , Prove that dy -1 %3D dx /1-x²

A:

Q: of y = In || dx 4 1-cos x 1. 1+cos x Find the

A:

Q: A particular solution for y +2y +y=1-cosX

A:

Q: 7 Find (b) x siny-ycosx-y = 1. dx

A:

Q: 3 Differentiate: y = In cosh° (cos 2x)

A: As we know that: The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1 From the given problem:…

Q: 4 sin (In t) cos`(1nt) dt 5.

A:

Q: (2e" sin(y) – 4y)dr + (–7x - e cos(3)dy = 0 not exact

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.