26 csc (2x) cot(2x) dx (Use Substitution Method) 26 26 + C 4 sin (2x) 4 2 26 26 + C 4 sin? (2æ) 4 26 26 + C 4 cot2 (2a) - 4 26 26 +C 4 cos2(2x) 4

Q: 2 sin A 1- cos A + sin A is equal to - then 1+ cos A+ sin A If y = 1+ sin A 1 y y O Option 1 O…

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Q: 5) cos A 30 B 16 34 7) sin Z 32 40 24 x, 9) cos Z 24 30 x,

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Q: 2 1. (2{cos z = (2(com(금)+i sin())" ti sin( - 3 3 1+v3i 2.

A: Solution 1: Given 5∠π42 Here…

Q: a. Z1 Z2 = r1 r2 [cos(0, + 02) + j sin(0, + 02)] %3D Z1 =" [cos(0, - 02) +j sin(01 – 02)] b. | | Z2…

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Q: sin 0 cos Od0 -u'du FC = - 1 cos“ 0 + C 19.

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Q: P H2) = 3 (13) flx)- Sin () (x3-3x6x-8) 1. (15) Cos x %3D f66)=Sinx. +cosx 18 sinseti (19) 20)…

A: (1)f(x)=3xAs we know that domain is the set of possible input values shown on the x axiswhile range…

Q: gral. cos 7x cos 4x dx ㅇ응 cos 3x + 숲 cos 11x + C ㅇ sin 3x + sin 11x+C 1 sin 3x - sin 11x +C

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Q: A B O A OB O OD 1 13 (sin(3z))¹⁰ + C 1 33 ſ cos(3z)sin¹⁰(3z) dz 1 3 (cos (3z))¹¹ + C F None of the…

A: Here we have to find the integral.

Q: | cos(Vx) dx A 2 Vx sin (Vx) - 2 cos ( Vx) + C C 2 Vx sin x (Vx) - 2 cos (Vx) + C B 2 Vx sin (Vx) +…

A: To evaluate: I=∫cos xdx Substitute x=u⇒12xdx=du⇒dx=2udu So, I=∫cos u 2u du=2∫u cos u du

Q: [sin³() cos(4) dx (A B C) D 32 32 3/² cos (4) + 3 cos (4) + C 5 32 3 cos (4)[-5cos² (4)+7] 35 32 35…

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Q: | 12 csc² (62) cot(6) dæ = 12 csc (6x) cot(6x) dx : (Use Substitution Method) %3D 12 12 +C 12 sin?…

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Q: S A. sinxcosxdx √esc²x-1 2 B. 7 COS X 7 5 COS X 5 5 cos³x x + C X 5 7 COS X 7 +C C. D. sin7 x 7 5…

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Q: ſcos (x/2) cos (x/3) dx * 3/5 sin(x/6) + 3 sin(5x/6) + C None of the choices 3/5 sin(5x/6) + 3…

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Q: sin³ (cos(4) dx 2 32 Ⓒcos A COS 35 32 B 35 32 Ⓒ-3 cos (4) C 32 D 3/7/7 C (4)[-5cos (4)+7] 5³ (4)…

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Q: Sin 2Q=20=2 sin a casa A 3 2.1.2√3/3 X=2√3 x=√√√3²-12 =√8=3√2 COD=

A: Follow next step

Q: |5x sinx dr = - 5x cosx +5 sinx +c OA. 5x cosr +5 sinr +c В. None 5x cosr - 5 sinx +c OD.

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Q: 1. The expression sin(x +y) +sin(x-y) is equal to A. 2 sinx siny B. 2 sinx cosy C. 2 cosx siny D.…

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Q: (1+sinx)9 cos x dx , u=1+sinx is The values of a. (1+sinx) 10 + C 10 b. (1+sinx)10+ c 1 (sinx)10+c…

A: Solution: The objective is to find the value of the given integral

Q: ƒ cos(x³) x² dx. 1 ¹ cos4 + c 4 1 WIT 3 1 -| sin x³+ C 1 ·cosª + c 4 4 -3 sin x³+ C

A: Topic = Integration

Q: 9 sin sin 2O° =Y 1o) cos cos 70 = a4 24 1)Sin Sin 7o = X 24 12) cos cos 20 = _ x %3D 24 24 20

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Q: A particular solution for y +2y +y 1-cosx Select one: a. A+Bx cosx +Cx sinx b. A + B x2 + C cosx + D…

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Q: Q.3) 3+4x+20 dx = a) Q.4) f sin5x sin4x dx = tan-(+) 4 a) = (cosx - cos9x 9 cos9x c) (cosx +°%$*) +…

A: ∫1x2+4x+20dx∫sin5xsin4xdx

Q: esin 2x [In (cos 2a)]? 2esin 2( cos 2x In (cos 2x) + 2 tan 2] 2esin 2a (cos 2x ln (cos 2x) + 2 tan…

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Q: St' sin(2t*)dt (sin(2t*) - 2t*cos (2t*)) + C (sin(2t*)-2t cos (2r*)) +C 14 1 (sin(2t*)-2t cos (2t*))…

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Q: | cos(V) dx 2 Vx sin (Vx)-2 cos (Vx)+C C 2 Vx sin x (Vx)-2 cos (Vx) + C 2 Vx sin (Vx) + 2 cos (Vx) +…

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Q: 5. у %3D sin?(3x? — 1) 6. Р() %3D 4csc(sin3t) ans. y' = 6xsin(6x² – 2) ans. P'(t) =…

A: Topic = Derivative

Q: у" + 25у %3D 0, у(0) 3 6, у'(0) 3D —4 Y(x) = | 5 cos( 5x) – sin(5x) sin (5x) x

A: We have given differential equation y"+25y=0 with initial conditions y(0) =6, y'(0) =-4 We have to…

Q: ſcos(5x-8)cx O a. cos ec(5x – 8) +c O b. sec (5x – 8) +c O c.- sin(5x-8) +c 5 O d. sin(5x-8) +c 5

A: Please refer the attached image for complete solution.

Q: = 4u ,u (0, y) =u (5, y)=u(x,0)= 0, u, (x,0)= 3, sin 27x - 2 sin 57x ,y >0, 0<x <5 70.3

A: Given                                            uyy=4uxx,   u(0,y)=u(5,y)=u(x,0)=0, uy(x,0)=3,…

Q: Cos dx 32 osSsin) +2+c (주)-5cos주)+ 기+ C 35 32 -cos 35 32 cos 7 (2)- 32 cos(수)+C +C 4 Cos COS

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Q: cos 3z 3 cos 2z cos z = 2

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Q: sin 4t sin 2t dt 1 sin 6t + C 12 cos 6t + C sin 2t + B) sin 2t 1 · sin 6t + C 12 D) 1 sin 2t + C 12…

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Q: cos2x – sin2x cos2x - dr = -F(x)+C. What is Fx)? 19. For cosx – sinx 3 A. (cscr - secr)3 2 2 sinx -…

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Q: Cose r(/2) =-1 (1+ cos e) dr – (sın²@ +sin2o cose - rsino LINE 1 |1. dr Sin o + sin20 ase - rsino…

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Q: y sin 2x + cos 2y = ax Find y' a – y cos 2x y% = sin 2x – sin 2y а - 2у сos 2x y sin 2x – 2 sin 2y…

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Q: |5x sinx dr = 5x cosx +5 sinx +c -5x cosr +5 sinx +c None 5x cosr - 5 sinx +c

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Q: Quèstion 3 8+11x dx = 8-11x %3D 1 1 1 O A. 2 + C ++11x 8-11x 11x OB. tan-1 8 64 121x + C |- 1 11x 8…

A: Multiply by sqrt(8+11x) in denominator and numerator.

Q: 1. у %3D х3 — х?cosx + 2xsic 2 sin x – 1 2. у%3D cosx+ 2 3. tan(xy) + xу %3D 0 4. у %3D хсоsх

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Q: 6. ans. -2cos(1/2)x + C 2 Scos3xdx 7. ans. (1/3)sin3x + C . Stan2vdk 8. ans. (1/2)In(sinx?) + C

A: As per the company guidelines we can solve first three parts. I hope that the given solution will…

Q: 6. 7. 3+6s+45²-25³ s² (s² + 3) 26-5²- s(s² + 4s+13) [2+1+√√3 sin √√3t-4 cos √√3t] 2 [2-3e-2t cos 3t…

A: To find the inverse laplace of the following.6 3+6s+4s2-2s3s2s2+37 26-s2ss2+4s+13

Q: Əz and Əx az #4. Calculate given that ду x² sin (z) + (x² – 1) y* = 2°.

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Q: 9. ytan x² a. 2xsec³² 10. y=sin x + 5 cos x a. posx–5sinx b. 5 cosx+sinx b. 2x sec 2 x² c. xsec²x²…

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Q: J (sin 3x)² = sin 3x xp- sin 3x CO = sin 3x xp- sin 3x On simplifying further, y2 (x) = cq sin 3x /…

A: In this question , constant is to be included in the last solution of the differential equation.…

Q: cotx sinx + cotx= 0 O +n + 2nx O 0+n5, + 2n a O 0+2,- + 2n A 2 + 2n 7

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Q: sin 5x sin adx =? O A, sin 4x sin 6x +c 6 4 sin 4x sin 6x OB. 8. +c 12 O C cos 4x 8 cos 6z +c 12 O D…

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Q: ∫0π/2[√(cos3x) sin3xdx]

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Q: 2csc 0--cos Ocsc 0 + cos 0+2csc 0 a 5x Sa 7a A) 4 3 4 3n B) 0, 4 7x 4 T 37 C) 2 2 3 5x D) 2 3

A: cosθ=0 implies θ= (2n-1)π/2 , n is any integer. cscθ= 1 implies, θ=(4n+1)π/2 , n is any integer.

Q: 6. ху\ + (1+х)y %3Dе*, у(1) — 0 7. sinx y'+2y cosx = sin2x, y : 2 6.

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Q: 1+sin A cos 2 sec u – cos µ = sin µ tan µ 4. + 2 sec 1 %3D cos A 1+sin A

A: We have to verify the given identities.

Q: sin 2 2) = (9z + 4), h(3) (2) (1) = sin(cos r), f"(1) %3D

A: