dr (g) sin(2x) + 4 sin r

Q: a- S 3ln²x_dx b- f sin5x.cos²x.dx

A:

Q: Find the general solution of f' (x) = -2x sin x2.

A: We have given the differential equation f'(x)=-2x sin x2. To find its general solution, integrate…

Q: 111. f (x) = sin 8x, (, 0)

A: We have the function f(x)=sin 8x In the point, the x coordinate is missing. To find the value of x,…

Q: 2 f sinx x2sinx + 2x cosx – 2 sinx dx + C

A:

Q: Evaluate the integrals

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Q: 4si 2xcos²x dx sin2xcos2x

A: It is given that,     ∫4 sin2xcos2xsin2xcos2x dx We have to evaluate it.

Q: 2 sin x dx cos x 7.

A:

Q: y = [x + (x + sin2(x))ª]³ %3D

A:

Q: COs 2.r dx x² + 2x + 2

A: In this question, we find the principal value of the integral by using residue theorem

Q: y = x* – 2x2 – 1 y = sinx sin2x

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Q: 3) (x²D² - 2xD+21)y=x³ sin

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Q: y" – 3y' - 4y = 3ez* у" - Зу'- 4у 2 sin x

A:

Q: y = sin(3 – 4x)" %3D

A: Apply the chain rule of derivatives, If y = f(g(x)), thendydx=d(f(g(x))d(g(x))×d(g(x))dx

Q: b) √ ²x³-x+4 dx x3 7T 4 (sin X

A:

Q: x Sin ( 3x- 2 |

A: Given: ∫ xsin3x-2dx   So, =-13xcos3x-2-∫…

Q: cos2r – sin2x cos2x F(x) +C• What is Fx)? For dx= 3 cosx - sinx

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Q: a) Find for 5x² – x³ sin y + 5e*y = 10 dx

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Q: y³x2 + yx³ - 20y² – 10y = 0 sin(x?) = cos(y³)

A:

Q: π/2 sin3 (4 ) αθ - π/2

A: To evaluate the following integrals

Q: 4)y = 2 sin (3x +) - 1

A: Given: y=2sin3x+π5-1

Q: EVALUATE Зд - 2 (c) dr x2-6x+ 8 EVALUATE sin-1x dx V1-x2 (d)

A:

Q: 2x+5 dx = AV7- 6x - x2 + B sin - (**)- 1. Vア-6xーx2 +C

A: ∫2x+57-6x-x2

Q: fim Sin (x-1) メキX-2 2

A: We have to evaluate limx→1sinx−1x2+x−2. If we substitute the limit then it is of the form 00, which…

Q: f(x) = sin 23x %3D

A:

Q: sin(7x 2) dx cos2 (7x 2)

A: Let u=cos(7x+2)differentiate both sides w.r.t. x.Use chain rule for cos(7x+2)From there we get du/-7…

Q: 2r sin 1 (r²) d»

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Q: dx sin-1x +c using method V1 – x2

A: Given:

Q: 2 sin (3x) d%

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Q: Solve (D² - 2D + 5) y = sin (2x) + 17x cos (2x) — 15x -

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Q: 3x 2. y = Ae³x cos x+Be³x sinx

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Q: What is the midline equation of y = -4 sin (2x-7)+3?

A: Given y=- 4 sin (2x-7)+3

Q: /2 Evaluate : | sin x dx. -/2

A: For the detailed solution of the problem follow the next step.

Q: 2. y = ₁³x cos x + c₂e³ 3x Ge 3x sinx

A: Find out the differential equation by elimination of arbitrary constants.

Q: Solve sin - () 2 dy = x + y

A: We need to use substitution method to solve this differential equation

Q: 13. (D² -1)y = x³ sin 3x

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Q: f(x) = (sin 3x)*² %3D

A: The given function is as follows. Rewrite the given equation as follows.

Q: y = sin² (3x)

A: Topic = Derivative

Q: y = sin(2x – 27)+1

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Q: Q3/ Find ∫ √x * Sin2 (x3/2-1) dx=? (by substitution)

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Q: Evaluate the integrals

A: Given integral, ∫π23π41-sin2x dx

Q: 2- Se2* sin x dx

A: ∫e2xsin(x)dxWe will use integration by parts: ∫fg'=fg-∫f'gf=sin(x),…

Q: find δƒ/δx and δƒ/δy. ƒ(x, y) = sin2 (x - 3y)

A: Given: fx,y=sin2x-3y  To find: ∂f∂x,∂f∂y

Q: Solve the equation for x in terms of y if 0 < x < π and 0 < y < π.4/sin x = 7/ sin y

A: using sin and cosine basic properties and applying some basic logic we have to solve the question.

Q: a²-x2 6- Sº, S dy dx -Va2-x2 7- Sx? cos 5 x dx

A: As per bartelby guidelines we have permitted answer only one question if given more than one…

Q: Find (f-1)'(a). f(x) = 2x3 + 4 sin x + 2 cos x, a = 2 (f=1)'(a) =

A:

Q: Find y' at the point (4, 4) where x sin(x² – y²) + 13 = x² – 3. -

A: y = f(x) g(x) Then y' = f'(x) g(x) + f(x) g'(x).

Q: cos2x – sin2x cos2x F(x) +C. What is F(M)? For dx%3D cosx – sinx 3

A: A detailed solution is given below

Q: f(x) = 8x + 6x – sin(x), 0) =

A: Derivative: f(x)=8x5+6x-sinxWe know ddx(xn)=n.xn-1ddx(sinx)=cosx

Q: y" -gy = 3e* + x - sin4x %3D

A:

Q: (2D – 5)y = sin 2x – 7 cos 2x -

A: