tan X dx = - I+ tan?x ! cor 2x tc 4

Q: sin (t) -dt 3 (4+ cos (t))?

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Q: 3." x cos? y dx + tan y dy = 0 x? cos? y +1 k cos y 4.

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Q: d²y Find С. dx? 1. y= sin 2x +cos² x sin x 2. у- - y= 1-cosx

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Q: 2. cos?x dx =x+ sin 2x + C X_SO

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Q: dx- B- If y = cos*x – sin*x , prove that: - d²y = -4cos2x dx²

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Q: Differentiate y= e*cos (x²): y = A e(cos(x?) – 2xsin(x?)) B -2xe"sin(x?) (c) e*cos(x²) – 2 xsin(x²)…

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Q: a. sin y i + cos x b. хyz (хі+уј+zk)

A: Note that : Curl of the vector field describes it's rotation.

Q: y (-1, 1) sin(e) cos(e) ante

A: The coordinate (-1,1) is in second quadrant in the below figure. The perpendicular is 1 unit, base…

Q: Q. It sin x Cos X XCOS xQ /- sin xd 3.

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Q: a) y' +sin x cosx = 0 y(n) = -2 %3D

A: according to our terms and condition i have solved question 6a for other question repost

Q: 3 dx = cos? 3x tan 3x 3 3 tan 3x +c tan 3.x +c попе

A: We have to evaluate the integral ∫3cos23xdx.

Q: cos z dz (4 + sin z)?

A: The solution of above integral is written in below steps.

Q: (c) sin(3x) sin(x)dx

A: Evaluate :   ∫sin(3x)sin(x) dx

Q: 4. sec? x tan y dx + sec? y tan xr dy = 0 Ans. tan x tan y = C

A: Solution:Givensec2x tan y dx+ sec2y tan x dy=0Formula:ddxtan x=sec2 x∫f'(x)f(x)dx=ln f(x)+Cln ab=ln…

Q: cos e de V1 – sin 0

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Q: 2 cos x dx, 1+ sin x (c) t = sin r. 0.

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Q: a) (sinx + cos 2x)dx (+1) do b) S dx c) S (x+2)(x2-6x+5) 8 cot(In 8)

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Q: T Cos x-sin x Jr x² dx So

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Q: sec?x tan y dy + sec?y tan x dx = 0

A: Given equation is       sec2xtanydy + sec2ytanxdx = 0

Q: fo (9 cos(x) – 2 sec²(x)) dx

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Q: dx 2. S; 3 cos x+4 sin x

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Q: Using the substitution u = cos(2x), S sin (2x) cos (2x) dx %3D

A: The given integral is ∫sin52xcos32xdx.

Q: /4 sec? Vwdw a) b) sin 2.xcos xdx c) f tanh xdx

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

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Q: 1) [(sin? x- cos² x) dx 2) J dx 2

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Q: -. sin x cos? y dx + cos² x dy = 0; if x = and y =

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Q: 2. Integrate | sin x cos? x dx

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Q: |- tan x da 1+ tanx IH Gos ó x - e ) da メ「メナ dx

A: "Since you have posted a multiple questions, we will solve first question for you. To get remaining…

Q: .2. COS X sın.x.ços.Xdx

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Q: (z*sin - 2° cos 2y cos r2 y? dr+2xy cos ,dy = 0.

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Q: Find dy and simplify whenever possible. dx sec x+tan x 1. у 3 sec x-tan x 2. у 3 е * соs e * — sin e…

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Q: I sec25x dx = ? tan x +C 1/5 tan x +c 1/5 tan 8x +C

A: We will solve the problem

Q: 2 dx (a) t = tan x. %3D 5+4 cos 2x 0.

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Q: o. S÷dx 10. sin 3x 11. S- 1-cos 3x

A: As per your request we solved question no. 10 & 11 only

Q: a) [ sin³(2x) cos(2x)dx (a) [ Sin(+) dx (b) [ Sin(F) dx dx (2 + e*)? dx |2+e*

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Q: 2) sec?x tan y dy + sec?y tan x dx 0 Ans: cos 2x+ cos 2y = c

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Q: Find y' and y". y = cos(x?) y' - -sin (x²) ( 2x) y" =

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Q: sin?y dx + cos²x dy = 0 ; y (÷) =÷

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Q: The solution of Sinx dx - x sinx+ y cosx= 0 is (y– 1) sinx =? A C-x sinx B C+ x cosx с-х cosx D C+ x…

A: sinxdydx-xsinx+ycosx=0sinxdydx+ycosx=xsinxddx(ysinx)=xsinx

Q: 3 dx = cos? 3x попе 3 tan 3x +c tan 3x +c tan 3.x +c 3

A: We will solve the following.

Q: I sin(z) cos I) COS(2C (x) dx %3D

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Q: y 2+ TT 3 2 -2+ -37

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Q: 2 cos e de 2 V1 – sin 0

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Q: sin?x d Prove that 2sinx dx \(1+cosx)² (1+cosx)²

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Q: y = tan x sin (2x)+cos (2x) 2 y' = A sin (Bx) + Ccos(3x) 3. A = B = C =

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: L, 4x(1– x²)dx S 2 i) ii) -) dx ? (х + Sin?x

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Q: sec x dx cos(2x +a)+ COS a

A: Introduction :