π/2 sin3 (4 ) αθ - π/2 (-2) 3 1 dx Vx ух

Q: F(x) = 1+e siny x %3D -- = -15 e sin4X- se"co54X fca) = fco) = -8 R fくり) = fci-2) = 4.2398 > KMS %3D…

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Q: 6. y" + 3y'-2y e-2* [(4+20.x) cos 3x+ (26-32x) sin 3x]

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Q: dx dy -2xcsc 2y - 2x³ cos 2y sec 2y x² = sin 4y + (4y + C)2y

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Q: (a) [(0.6e15 + 4t 3t² +03-10-01 at 4t4-3t3 + 0.3 _10t 1.5 -0.1 2t3 (b) Evaluate…

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Q: 5 dx Find dx, x> V25x? -9 5x In 25x2-9 + C 3. sin-13x+c 1+9x2 +3x|+c 1 V1+9x? + C 3x 3. + C V25x2 -9…

A: The solution is given below in the next step:

Q: Q3- Find i) S sin3x.cos(-5x)dx

A: We have to evaluate the following integral: int sin 3x . cos (-5x) dx

Q: 3π/2 3) 14 cos 2x dx п/2

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Q: 1. 2. (D² -3D+2)y=sine-*

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Q: 2e**+11e3x+16e²x V. e2x+5ex+6 sin2x vi. S -dx cosx+cos*x-2cos²x

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Q: cos 2x 12) S 2cos2x sin x – sin x dx -

A: To integrate:∫cos2x2cos2xsinx-sinxdx Solution: ∫cos2x2cos2xsinx-sinxdx On simplifying further we…

Q: Scos2x (2 2 Cos 2X (2 cos 2X -1) dx

A: Given integral is ∫cos 2x2 cos22x-1dx To find: Value of the given integral. Formula used: 1) cos…

Q: 1. x siny + x²y = c 2. xy² – 1 = cy 3. x = A sin(wt + B), w a parameter, not to be eliminated -

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Q: |3 cos(2x – t/ 2) cos(x+ t/ 4)dx

A: To evaluate the integral: ∫3cos2x-π2cosx+π4dx Solution: We know that, cosa cosb=12cosa+b+cosa-b…

Q: 1. Determine the general solution of this equation in terms of C ( sin y- ysin x) dx + (cos x + x…

A: We have the following solution for given ODE:

Q: fe²x+Inx² sin x² dx = - +1/√√e²x cos x² dx

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Q: |3 cos 2.r dx 3.

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Q: 1. f/² sin () cos (+) sin (²) d dx (Consider initially the first 2 terms)

A: We have to use the formulas for 2sin(A)cos(B)-sin(A+B)+sin(A-B) and 2sin(A)sin(B)=cos(A-B)-cos(A+B).…

Q: 3 (a) | (7)dx (c) dx (sin x + 1)dx (b) L (x° + 2x + 1)dx (d) 0,

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Q: y = cos(2x), y = sin x, 0<x< 2

A: Solution is given below:

Q: •1/2 | cos(T(x + 1)) dx -2

A: First remove the upper limit and Lower limit and then substitute to make the problem simpler to…

Q: -2 S(V2r – 1)2 dr | cos(r) | dx COS

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Q: 2. The suitable Trignometric substitution that solves fx(x-2) dx is (x-1)=sin 0 x-1)3sec0 (x-1)=tan…

A: We can find the answer as below.

Q: 3. 4. 5. π X dx sin() co₂ (:) ª 2x - 1 4x1 dx 8. 9. (x-1) √x dx _2_2x dx 10. S√₁-2² a x dx

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Q: 3) f₁ dx do - cos 0

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: -2/√√/3 dx x√√x²-1 • [²/²2 (x + 12/²3). dx sin² π/6 28. • √2 30.

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Q: [(cos 2y) – 3x?y²] dx + [(cos 2y) – 2x(sin 2y) – 2x³y] dy = 0 %3D

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Q: 2x 2)/3x* 2) [3x* - 9x² +1 V9-x² dx .2 3) [ sin xcosx dx x cos.x 4) S sin² xcos 4) sin x cos x dx

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Q: 1) S“(cosx)" dx. 2) Г(-4). 3) В (10,9) 4) Sº x° e-2* dx Ja-x)i 5) o

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Q: 3 x* cos(3 y) 2 x³ sin(3 y) dx + + 2 x2 ) dy = 0

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Q: dt 1. cos (2 sin 2r) V1-4r

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Q: x³ + y³ + 3 x² siny tan z = 5 az dz and əx Find ду

A: Given,          x3+y3+3x2sinytanz=5

Q: 5. (4xy-y²+10x²+sin x)dx+(2x²-2xy+ cos y )dy=0

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Q: x cos x² 2. X C0 dx -siny

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Q: 2. cos æ /1+ cos² x dx dy =? Jsin=' y -2/2 (a) 1 3 3 2/2 (b) 1 3 -2/2 1 (c) + 3 3 2/2 (d) 1 3 V2 (e)…

A: Properties of integartion  To determine ∫f(g(x))g'(x)dx Put t=g(x) the integral will be…

Q: æ' = y – 5 sin (3t); y/ = -4x + 17 cos (3t) , ift = n, x = 7; y = -4

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Q: B sin 5x+ sin 3x 1 sin 5x+-sin 3x+c 6 I 10 fcos 4x cos.x dx = ?

A: Given :∫cosxcos4xdx

Q: [2xy cos(x²) – 2xy + 1]dx + [sin(x²) – x²]dy = 0

A: The solution attached :

Q: 3T/2 1|sin(x| dx 01

A: Topic = Integration   using this definationsin x=sin xif 0≤x≤π-sin xif π&lt;x≤2π

Q: Q-4) Find the general solution of the Cauchy-Euler equation x'y"+ xy'+4y = sin(In x)

A: Solve the Cauchy Euler differential equation

Q: 11.| V1- сos 2x dx COS

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Q: 2. [ (1–3x)sin(}x)dx 4w dw 3. [* w°e™ dw w²e* -1

A: This question is taken from the definite integral in which we have to find the integral of the given…

Q: 4) e (). – | T|x² – 4| CoS - 2 2x sin sin² ( T|x² 19 dx 2 -3

A: Integrate

Q: Find dy/dx of: x3 - sin y = (1/x3) + tan-1 (ey) - π/4 Don't simplify the final answer.

A: Given:     To determine:

Q: y" – 2y' + y = [-6x – 8] cos(2.x) + [8x – 11]sin(() 2x) %3D

A: We have to solve the differential equation y''-2y'+y=[-6x-8]cos2x+[8x-11]sin2x.

Q: e-3t sin (4t) y (0) ==

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Q: cos (2t) 23. sin' (2t) dt 3

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Q: 31. (a) |2x - 1| dx (b) 3π/4 1.T CT/2 \cos x dx

A: