Find L{10) } s(s²+16) 1+cos(4t) 16 1-cos(4t) 4. 1-cos(4t) 16 1+sin(4t) 4 1-sin(4t) 16

Q: 10. Show that 2" + 42' + 8z = 0 if z = e-2=(sin 2x + cos 2x).

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Q: 19. Evaluate the following sin³ [sin³ (2) cos(4) dx 32 A. 35 COS 5( 4 ) [-5cos² (4)+7] -cos 32 32 -…

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Q: The f sin 2x cos 2x dx is 1+3 cos 4x 1 sin²4x + C 24 1 In|1 + 3 cos 4x| + C 12 {A} {B} {C} - In|1 +…

A: To find the value of the given integral ∫sin2xcos2x1+3cos4xdx using substitution

Q: If e /2i =sin2 then z = 2i In(sin2) + 4k TI - 2i In(sin2) – 4k TI - - 2i In(sin2) + 4k TI - -2…

A: Use the principal log to find z.

Q: | cos(5x) sin(13x)dx = 1 sin(&x) ) sin(18x 4 6. OB. - 5 sin(5x) sin(13x) + 13 cos(5x) 1 cos(1&x)…

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Q: sinx S- cos?x+ 6cosx+13 O In cosx+3-Vcos²x+6cosx+13|+C O In cosx+3+/cos²x+6cosx+ 13 O…

A: To find:

Q: "(등 -2) + ain (품 + 22) The simplified form of cos 22x) + sin O V3 cos 22x + sin 22x O v2 cos 22x + 2…

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Q: Find * sin (In æ) cos²(ln x) dx. cos (In x) , cos³ (In x) 3 cos (In x), cos³ (In x) 5 3 5 Option 3…

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Q: Find where z = sin (x²) cos (y) COS © 6.x sin (x²) cos (y²) COS 2.x sin (2²) 2x cos 2.x sin (x²) cos…

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Q: 1 L-1 s(s² + 4). 1 1 [1+ sin(2t)] 2 [1 – cos(2t)] | Option 1 O Option 1 1 1 [1+ cos(2t)] 4 [1 –…

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Q: [10 sin(2x) cos(2x) √ cos²(2x)-5 dx O a. 5 (cos² (2x)-5) ³/5 + C 3 5 O b. -(cos² (2x)-5)³/2 + C OC.…

A: To evaluate the given integral.

Q: Find L {(2- t) (5 cos 3t 1)}. - 5(s²+9) (s² –9)² 10s - 82-9 5(s2-9) 10s - - s2 s2+9 (s²+9)² 10 82…

A: As we know from the Laplace transformation; 1). La·ft+b·gt=a·Lft+b·Lgt 2). Ltnft=-1ndndsnLft And…

Q: Evaluate sin 2x sin 4.xdx 2 b. sin 3 2x + C 3 1 a. sin ' 2x+C 3 c. cos' 2x+C 1 с. 3 d. -cos 2x +С 2

A: To evaluate the given integral: ∫sin 2x sin 4x dx

Q: Find L{(t- 1) (2 - 5 sin 3t)}. 15 30s s2+9 (s²+9)? 2 15 15 s2 (s²+9) s(s² +9) 15 15 3-号- 3? (s²–9)…

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Q: Evaluate: 8 sin xcos xcos 2.xdx -cos 2x- 1 cos 2x +C 10 8 cos 2x--cos 2x +C С. A. 14 1 -cos 2x 10 1…

A: Integration is generally used to calculate area under the curve. When function definition changes…

Q: Find L{(1 – t) (3 + 2 sin 5t)} . 3 2s 10s - 82+25 (s2 –25)² - 10 20s 을 + - - s2+25 (s² +25)² 3 3 10…

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Q: 5. Find all solutions of 2 cos x- -cos x-1 0 if 0sxs2n.

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

Q: Compute 2° sin(x" + 2) dæ. O -7 cos(x" + 2) + C O 1 cos(x² + 2) + C O - cos(2" + 2) +C 1 cos(2" + 2)…

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Q: 24. Evaluate: S(cos 2x) esin 2x dx A. -e sinzx + C esinzx +C C. esinzx + C esinzx D. + C В.…

A: using substitution method to solve integration

Q: S cos(3r)(sin(3x) +5)10 dz Select one: (sin(3z)+5)" 11 +C O (sin(3r) + 5)"+C (sin(37)+5)" 33 +C…

A: Consider the integral: I=∫cos3xsin3x+510dx……1

Q: sin In 4+tan cos-dx 4+tan-Icos- 2 1+ cos 2sin In4 4+ tan cos- dx A 1+cos 4+ tan-cos- 2sin-In 4+…

A: To rewrite the given integral so that the integral can be evaluated easily. ∫sin…

Q: Š 4 sin(3t) 2+ cos(3t) 7 sin(3t) + dt (2+ cos(3t))²

A: Definite integration

Q: The simplified form of cos ( - 5z) 5z) + sin 6 52) + sin (; + 52) O v3 cos 5x + v2 sin 5x O v2 cos…

A: This can be evaluated as:

Q: L- ( In s4 (s2+9)(s²+4) + cos 2t + sin 3t cos 2t+cos 3t - t 2 cos 2t – 2 sin 3t | sin 2t + cos 3t -…

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Q: coS(T/11)-cos(2t/11)+cos(3t/11)-cos(4Tt/11)+cos(5rt/11)=?

A: To determine the value of the below expression. cosπ11−cos2π11+cos3π11−cos4π11+cos5π11

Q: 8. 5 cos²x - 3tan x COS X dx

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Q: Evaluate. de (sin(5x – 1)] cos(5æ – 1) 5 - sin(5æ – 1) 5 · cos(5æ – 1) • 5· cos(x)

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Q: If 1, = |x" sin8x dx , Then 64 I,+n(n-1) I,-2 Select one: O- 8x" cos8x +n x" 7 sin8x O + 8x" cos8x…

A: Given :  In=∫xnsin8xdx                1 Using Integration by parts…

Q: 1- cos 2x 2 1+ cos 2x 1 (1- cos? 2x)(1+cos 2x) dx = 8. 8.3.25 sin2 z cos a dx = 1+ 8 dx = cos 2x -…

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Q: Find L{(t – 1) (2 – 5 sin 3t)} . O 2 5s 30s - 82+9 (s2 -9)² 2 15 15 - - s2 (s² –9) $(s2-9) 15 15 2…

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Q: 17. If 4 sin x+3 0 on 0 sx < 211, then x=

A: We have to find x if 4 sin x+3=0 on 0≤x≤2π. Solving the given trigonometric equation, 4 sin x+3=04…

Q: C 3y° cos xydydx = O 3(1-Cos3) 5(1-cos3) cos3-1 O 5(1-Cos3)

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Q: - Find all solutions for 4 cos x+V3 = 2 cos x if 0<x<2n. %3D

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Q: 1 what are possible values of cos x and tanx? 2 If sinx= Select one: V3 and tanx= 2 1 a. cosx= V3 V3…

A: Consider the right triangle with one angle x degree. Let a be the length of the adjacent side and b…

Q: 3. tane de ) 71+ n cose)/3

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Q: L= {4 sin (3t) + 2 cos (9t)} L = {sin (2t) cos (2t)} 4s 6 2 + s2+1 s2 –9 s2+4 4s 6 + 82+1 2 s2+9…

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Q: Which of the following is true? J sin(3x)sin(4x)dx = cos(x) – cos(7x) dx 2 ® Jsin(3x)cos(4x)dx = […

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Q: я/4 4 sin (4t) dt. 9- cos (4t) Evaluate the integral я/4 4 sin (4t) dt%3D 9- cos (4t)

A: Use integration by parts

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: Which of the following is true? A Jsin(3x)cos(4x)dx= [ Sin(7x) – sin(x) Jcos(3x)cos(4x)dx= [cos(x) +…

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Q: Given: z = sin 3x cos 4y Find: z ду2 -3 cos 3x sin 4y -9 sin 3x cos 4y -12 cos 3x sin 4y -16 sin 3x…

A: Differentiate the given function partially w.r.t y keeping x as constant   ∂z∂y=sin 3x×4-sin 4y…

Q: Find , if da y = 3x cos4x 12x* sin4x – 10x cos4x None -2x4sin4x – 12x° cos4x -12x4 sin4x + 12x°…

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Q: Compute sin (3r)dr (25z4+1)2 -

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Q: Find 2 if x? cos4 cos* T. 1) 2xcos x+4x2cos3xsinx 2) 2xcos x- 4x²cos³xsinx O3) 2xsinx sin xcosx 4)…

A: Hence option (2) is correct.

Q: L-' (In (s²+25)(s²+16) cos 5t-cos 4i O -2 cos 2t – 2 cos 31 O 2 cos 5t – 2 sin 4t sin 4t-cos 5i t…

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Q: Z {sin(3t + 2)} O (5 sin (3) + 2cos (3))/ (s^2 + 4) O (s sin (3) + 2cos (3))/ (s^2 + 4) (s sin (2) +…

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Q: The simplified form of cos G- 13x) + sin + 13x V2 cos 13z + 2 sin 13æ O v3 cos 13z + sin 13x O cos…

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Q: Find L-1 s2+4s+29 cos(5t) -cos(5t) O 15 cos(5t) – 2 sin(5t)] - O sin(5t)

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Q: 6. Show that in the interval (0, 7) 4 cos 2nx sinx = 元 Σ 4n2 -1

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