1I) (3y cos(3x)dx-sin(3x)dy)/ y 0

Q: s sin(3x) + cos(5x) – sin sin)ax |dx

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Q: Determine 1 dx , 4x2 +1 (i) (ii) x cos x dx .

A: Determine.  (i).  ∫14x2+1dx             ⇒∫14x2+1dx=14∫1x2+14dx  ⇒∫14x2+1dx=14∫1x2+122dx…

Q: Find dy. y = tan H 4 X + cos(4x)

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Q: te √e³x Evaluate 3x cos 4x dx.

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Q: 2. f cos³ (20x)dx

A: Given :

Q: (y cos x + 2xe)dx + (sin x + x²ey – 1)dy = 0

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Q: cos 2x dx (b) 4 cos t dt 0 2

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: 7 Sin (3x) Sin (5x) dx

A: The objective is to evaluate the integral ∫0xsin(3x)sin(5x)dx Use the trigonometry formula:…

Q: TT b) F /1- 1 – cos (2x) dx 2

A: Topic-Integration

Q: z = sin(6x) sin(5y) az az dy II

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Q: Let y = cos(2x) 9x²+3 Calculate dy dx

A: Given function, y=cos(2x)9x2+3

Q: X dy + dx dy Y dx 2 - 1 sin(2x) = r arcsin(r)y5 (1 - cos(2x)) y³ y = (1

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

Q: Solve dy dx + y tan x = -y³x sec²(x)

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Q: Calculate ㅠ 2 6³ cos² (4x) sin² (4x) dx

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Q: If y = cos 3X find dy/dx: y = cos?3x = (cos 3x?. (cos 3x )?. %3D

A: Given, y=cos23x=cos3x2

Q: S(6Vx + 3 cos x - 8)dx

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Q: Jsin(x)cos(x² + 7)dx 2 2

A: Solving the problem

Q: dy Find dx if y = cos (4x - 3x + 1) s*(4x²-3x + 1)

A: Given that, y=cos4(4x2-3x+1)

Q: 3y?r + sin(2y – 4) = V(2y)

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Q: d dr -x² + e³¹ - tan(x) dy²-sin(y) dy cos(y) +2 d dx -√x+e²

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Q: S sin(3x + 2) cos(1 – 4x)dx

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Q: 1/2 sin 12 y cos' y dy y

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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: // (cos (a? + y³)dA where D: {(x, y) | 4 < x² + y² < 49} Find

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Q: dy Find if y= tan( 2x+5) dx

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Q: 3+6 b. (2xy-sin x) dx + (x-Cos yldy

A: Topic:- solution of differential equations

Q: sin?y dx + cos²x dy = 0 ; y (÷) =÷

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