2 X 1 t3 COS 4- x² dx 2 -2

Q: 3 (b) / 2³ x³ cos(x¹ + 2) dx

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Q: T/3 4 sin x -dx 1-4cosx

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Q: Find integral.

A: ∫-11xcos x dx

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

A:

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A: Given that: ∫x29-x2dx

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A:

Q: 1 COS x dx X - sin x | C. #55. 2)

A:

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

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Q: 6. (a) cos 2x dx; u = 2x

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Q: d. cos 3x = 0 %3D e. tan 4x - 1 = 0

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Q: COs 2.r dx x² + 2x + 2

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

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

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

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Q: 37/2 8 cos x dx T/2

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Q: 10) Solve xy' = y+ 3x* cos y(1) = 0, x = 0.

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Q: 3 п 2 2 cos² 4x dx

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Q: 4 sin x dx (1 + cos x)²

A: Here we have to solve the given integration.

Q: 4) y-3y'+2y =e"(1+ cos 2x).

A: First we find out C.F. and then we find out P.I. and then the complete solution is y=C.F.+P.I.

Q: (6e + 6x°+ 4 cos a + 2)dx 6e + x° + c 4 cos a + 2x +

A: Since this is a multiple question, according to the Bartleby answering rule, only first question is…

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: 1. i) Find ſcos 2x +3 sin 3x dx . ii) Evaluate fxe dx. Hence, solve | 5xe e dx. 1

A: To evaluate the given integrals.

Q: (x*+2 cos x -1+ 20) = 205) = dx %3D fuse rules)

A:

Q: 4. f cos? 2x 4. cos? 2x sin 2x dx 2 2 5. f sin¹¹ ²3x cos / x 3x dx

A:

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

A:

Q: d3 (2 sin x + 3 cos x Find dx3 x³).

A: Given that: d3dx3(2sinx+3cosx-x3)

Q: 1 X COS 2 4 – x² dx t3 -2

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Q: b) S. cos x cos 7x dx

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Q: cos x 3. f sin³x dx (2 + sin?x) + C 3 4. S* x sin 2x dx 1-9x2 5. S sin-1 3x dx + x sin-1 3x + C 3

A: Q - 3

Q: 3. 2 +X-1 dy 2=Sin (cos 8x) %3D

A: 1) Given that y=4x35-6x2+x2-1 y=4x35-5x2-1 we have to find the derivative of 'y' with respect to 'x'…

Q: 8. / (V80 – x² 0.3 cos(1.2x + 1.3) + 5) dx -

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Q: dy 2) x - 2y = x³ cos4x

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

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. The solution of the…

Q: 5. (y" – y) = e-X cos(3x) %3D

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

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: x² cos(3 x) dx

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Q: 3 2 พ 2 cos2 4x dx

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Q: 1 3 X° cos 4- x2 dx + 2 2

A: We will find the value of definite integral as following.

Q: 2 cos Vx = cos (2x-1) 0<xs1

A:

Q: k. [₂ x cos³ 2x sin 2x dx

A: According to the company rule we can answer only first question and rest can be reposted.

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: x6 cos(x³) |dx=0

A: Follow the procedure given below.

Q: 4x Cos x dx b.

A: Given :

Q: dx 5+4 cos x

A:

Q: -1 'Cos'¹x { √(1-x²) } ]¹_dx og. { 1 + (sin (2x√(1-x²))} TT

A: Given data:- ∫cos-1x1-x2-1loge1+sin2x1-x2πdx

Q: y = 15x cos X COS X %3D

A: Given that - y = 15xcosxDifferentiating on both sides with respect to x - y' = 15ddxxcosxy' =…

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

A:

Q: 5. S sin(3x)dx (a) 3cos(3x)+ C (b) †cos(3x)+ C (c) – 3cos(3x)+ C

A:

Q: dx 3+2 cos x

A: The value of the given integral is 2√5/5 Arctan[√5/5 tan(1/2 x)] + c