3) I = dx 4) 1 = S cos?x dx

Q: dx (2) S V9-x² E(Ctrl) X. 2x sin-1(구)+ sin-1 (민 + Option 1 Option 2 2x cos-1(민 + c CoS Option 3

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Q: 2 tan(4x-1)-3 cos² (4x-1) If we let u = 4x – 1 for the dx, what will be the resulting integrand?…

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Q: Find dy/dx for y = (cos x) 2 + sin(x 2 )

A: Given that      y = (cos x)2 + sin(x2) We have to find dy/dx .

Q: 18y sin3 9y2. 10) +3 cos V9y2 + 3 dy + 3 cos

A: See the attachment

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Q: If y=(sin3x-cos3x)², find dy dx

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Q: what is the antiderivative of   (sinx/1+cos2x) dx?

A: Let,

Q: tan (VT)+2 dx J Va (sec(VT) – cos(/7))

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Q: 1. Integrate: e3x cos(x) dx

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Q: 29. [sin (9y)sec (9y)dy

A: Use the formula sin2x + cos2x =1.

Q: Let 5 sin æ + 6 cos y = 6. dy dx d?y dx?

A: 5 sinx +6 cosy = 6  Differentiating w.r.t x,  5 cosx +6 (-siny) dy/dx = 0  dy/dx = 5cosx/(6siny)

Q: If given integrand is x² cos 2x dx and dv is equal to cos 2x dx, what is v?

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Q: 1 Evaluate [ (x³ +cos(3x))dx 2

A: The given integral is ∫x3+12cos3xdx.

Q: 3. If y = (sin 4x)², find y' %3D a.) 4 sin4x cos 4x b.) -4 sin4x cos 4x c.) -8 sin 4x cos 4x d.) 8…

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

Q: Compute dy/dx if sin(x) = cos(xy^2

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Q: S" sin" (0.5x)cos (0.5x)dx

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Q: 10. Find , if y = dy 1-cosx dx 1+cosx

A: Given  y = (1- cosx) /(1 +cosx) To find dy/dx

Q: 3+2cosx dx is equal to (2+3cosx) sin x 2 cosx 2+3cos x) 2+3sin x 2 cos x 2 sin x (d) 2+3cosx 2+3sin…

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Q: (雲) 1 dy tion 1+ is = 3 dx wy da 3, 1 12, 1 1, 15 15, 1

A: We have to choose the correct answer

Q: 1- d/dz [cosz] = -sin z

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Q: [ 2x sin (4x)dx O =cos (4x) + C -x² 4 2 sin (4x) + 8x cos (4x) + C sin (4x) – x cos (4x) + C ○중cos…

A: Integration by parts

Q: what is the acceleration at time t=o of a particle if its position is s(t)= cos (3t)-sin(4t

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Q: dt cos (2 sin 21) /1– 4r

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Q: One approach to evaluating 2 cos (2x)dx is to first rewrite it as cos(4x) + 1 dx а. cos(2x) – 1 dx…

A: This is the question of integration.

Q: = sin(5x) for y(0) = 2

A: the solution is, y = (11 - cos5x)/5  The detailed solution is as follows below:

Q: Flnd * |(sin 5x cos 3x + cos 5x sin 3x) dx cos 8x cos 3x + 3 cos5x – + c 8 + c Option 3 Option 2 cos…

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Q: (b) Show that 2t cos x and sin x = 1 + ? (c) Show that dt dx 1 +

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Q: 4: Find aun -2 2y² Sin(xy) dx dy

A: Topic:- application of integration

Q: 1. S cos (3 sin x)cos (4 sin x). cosxdx sec*x dx 2. Jtanx 3. Sr 6 tan*x dx 4. /2 sin5x dx

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Q: please solve determine dy/dx if xy = ecsch(xy)+πcos(0)

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Q: 5. Solve dy dy + y = 2sin(3x) dx - dx? using the method of undetermined coefficient.

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Q: S sin(3x + 2) cos(1 – 4x)dx

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Q: V3 with 0 < x < 2n. 2 cos 2x cos x – sin 2x sin x - -

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Q: 3z cos(z)dz

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Q: 4. Ify =/sin x+ /sin x+.to inf inity, dy _ cosx dx 2y-1 prove that

A: Derivative of Sinx is Cosx

Q: S" cos de 4. 2 dx .2 -1 1+x² 5.

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Q: If y = (sin-' x)², show that (1 – 2*) dy dr? dy 2. dx

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Q: 4 sin' 2x cos 4x dx 4.

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Q: z sin(2- 32)+cos(2 - 3a)+c | 4x cos(2 – 3x) dx 4x cos(3 3r) dx Option 1 Option 2 |4 cos(3- 3z) dr…

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Q: 4. [(3sin 2f – 3 cos 5t )dt 5. sin x dx cos x

A: 4) Given:            ∫3sin2t-3cos5tdt       =∫3sin2t dt-∫3cos5t dt taking constant out…

Q: 2.1 Given that 1 sinh x show that dy cosh a. dx

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Q: 1- Sinx + Cos2y=0 dy dx

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: 2) Integrate: S(29sinx + 6e + 5 cos x + Vx)dx

A: Given that, The integral ∫29 sinx +6ex +5 cosx+x5 dx By using ∫f(x)+g(x)dx =∫f(x) dx +∫g(x) dx ∫ 29…

Q: 2n Sin (3y) dx + 3x Cos(ay) dly =o

A: Given differential equation is 2xsin(3y)dx+3x2cos(3y)dy=0

Q: 1- LS7 cos(y)esin(y)+9x dydx 2

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Q: Suppose x and y are functions of a third variable t If sin2(x) + cos²(y) =- and dr dy what is the…

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Q: 2. sin3x dx + 2y cos³3x dy = 0

A: Given- sin3xdx+2ycos33xdy=0 To Solve- The above differential equation.

Q: 6. Vsin x sin 2xdx Vtan 4x 7. J cos² 4x 8. cos 2xsin 2.xdx |arctan(3 – x) - dx 9. 1+ (3-х)? 3e 2y…

A: Given