sin(2t + ) dt = 00 64e 4. O O OG

Q: 8. (t² + 3) cos(5t) dt

A:

Q: 33. sin x dx dy х 0,

A:

Q: (3t+t²)sin (2t)dt

A: We have to integrate the function        (3t + t2)sin(2t)

Q: 2. 2x?cos y dy + sin y ( x+ siny)dx

A:

Q: S V3x – I dx а. - b. f cos 7x dx J 2+sin x COS x dx с.

A: As per our guidelines we are supposed to answer only three subparts of a question. Kindly repost…

Q: 118 t' sin (2€) dt

A:

Q: dy 1. dx x(2 In x+1) siny+y cos y

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

Q: t sin(2t)dt.

A: Given : ∫tsin2tdt

Q: 4-1{ 1 s(s? + 4 ၂။ sin2t.dt

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

Q: ∫(3t+t²)sin⁡(2t)dt

A: Given that, the integral is ∫3t+t2sit2tdt.…

Q: Let y tan(5x + 8). Find the differential dy when I = 5 and dr 0.1 Find the differential dy when I 5…

A: y=tan(5x+8)Differentiate on both sidesdy=sec2(5x+8)×5×dxSubstitute x=5  , dx=0.1…

Q: 4x3 — 2х2 — х+5dx А. -2 TT 3 sin t 4 dt cos²t В.

A: Evaluate the integral using the second Fundamental theorem of calculus.…

Q: | t sin(2t) dt 1.

A:

Q: -2 cos(6t) dt J (10+4 sin(6t))²

A:

Q: (t² +3) cos(5t) dt

A: According to integration by parts:∫udv = uv _ ∫vduWhere u can be choose in the orderInverse, Log,…

Q: dt f(x) = 1+ sin? t

A:

Q: I 1 y sin(2²)dx dy. 0. y2

A: See the details solution in below

Q: 一3十 Sin zt dt

A: We have to use first shifting property and Laplace transform of integration property to Laplace…

Q: d(sin'xl: I dx VT-X2

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: rt%3Dr/6 t cos(2t) dt t=D0

A:

Q: V3x d. Evaluate dx sin(3t) dt

A:

Q: ACTÍVITY 2: Differentiate the 1) y = -2 sin 2) s (t) = - WE

A: Apply the differentiation rules for the trigonometric functions to get the derivatives of the given…

Q: Sot.e-3t. sin 2t . dt f(t)

A: Take the integral: integral e^(-3 t) t sin(2 t) dtFor the integrand e^(-3 t) t sin(2 t), integrate…

Q: dy Find dx 1/4 | sin (?) dt y =

A:

Q: Solve for the General Solution ds 5s = dt te 5t sin t %3D

A:

Q: ý + 16y = 8 (t – ) sin (2t), y(0) = 0, ÿ(0) = 0

A: The solution is given by using some formulas of Laplace transform as follows :

Q: L(cos at) = %3D s2 - a2 صواب İhi O

A: Given that  L(cosat)=s/(s^2-a^2) To find the condition is true or false

Q: d. t sin 2 dt COS dx 3

A:

Q: y = tan o (sin 67E-TT) find dy dt ()

A:

Q: d²y +9 = cos?t+ sin? t + cosh t + sinh t +3 sint -3t dt %3D dt2

A:

Q: dx + 3x dt cos(5t) %3D with x(0) = 1. x(t) = %3D

A: The given initial value problem is: dxdt+3x=cos(5t) ;         x(0)=1

Q: sint In(cos t)dt

A:

Q: 4. § xe¯ dx 6. |t sin 2t dt Jx² cos mx dx 8.

A:

Q: Solve the initial value problem. dy ху?- сosrsinx а. у (0) %3D 2 dx (1- x?)

A:

Q: 6. sin v- -2 cos Va + C %3D 4x2 1. Ja-8 dx = 18 (1-8x)4 (1-8x3)4 8. Se*dx =+ %3D In e

A: As per the instruction, we will be answering only the first three subparts. For (6),    ∫sinxxdxLet…

Q: I d²u dv² tan v sec“ V

A: Find your answer below

Q: (7 cos° t dt 2

A: ∫0π/2 cos9tdt ∫0π/2 cost(1-sin2t )4dt here lets substitute that sint = u du/dt = cost du = costdt…

Q: FCH)- O -t e Sin 2t dt

A: To find the below integral. ft=∫0te−tsin2tdt

Q: d's 元 =-4 sin 2t-- 2 s'(0) = 100,s(0) = 0 %3D dt?

A:

Q: 5. Find dt ,y = cos(sin(t – 4))

A: Given function is: y=cossint-4 Derivation of the above function with respect to t. dydt=ddtcossint-4

Q: Can you help me step by step?

A: Given information:

Q: dy Find dt y = tan ( sin (4t - 3))

A:

Q: 1.) dx = t (1 + t2) sec?x dt ans: 2x + sin2x = (1+ t?)² + c

A: Since you have posted multiple questions in this question i can do first question as per our company…

Q: Cos Vt dt 3. Evaluate

A: The integration of the given integral is; Cos√t/√t.

Q: dy 1 cos t + 1 dt 2 || ||

A:

Q: 1) I = ft e" dt 2) I = Se-2x sin 2x dx

A:

Q: d. a) dt [8 sin 1 2t] = d. b) |7 cos s 1 5 dx d. 3u] = -1 c) 10 sec du

A:

Q: tan-1 (xy)=3x2+sin-1(y) find dy/dt

A:

Q: D. ( [ 3° cos"(5t) dt sin(z)

A: