J (sin 3x)² = sin 3x xp- sin 3x CO = sin 3x xp- sin 3x On simplifying further, y2 (x) = cq sin 3x / cos ec?3xdx = -Co sin 3x= cot 3x 3 - sin 3x cos 3x sin 3x - cos 3x Therefore, y2 (x) = -cos 3x = C cos 3x [C = - II y2 (x) = cos 3x Hence, the second solution of the differential equation is у2 (х) %3D сos 3x.

Q: 2 sin 2x dx Vcos4 x + 4 cos² x – 2.

A: Given that, ∫2sin2xcos4x+4cos2x-2dx The trigonometry equation is, sin2x=2sinxcosx Take…

Q: 18. Evaluate ſe3 cos 2x sin 2x dx 1,3 cos 2x + C c.e3cos 2x + C B. -e3 cos 2x + C e3 cos 2x D. 6 sin…

A:

Q: 1. (2x4-x3-2x+3) dx 2. (3-2x)2 dx 3. 3(x-1)(2-3x) dx 4. (5-5x+x5) dx 5. 1/3 ex dx 6. (x2-cos x)…

A: The integration is an anti derivative process. it is reverse of the process of differentiation. Here…

Q: Find the iterative scheme for the root of equation cos x- 3x+1=0 by Newton-Raphson method. O a. None…

A: Newton rephson method problem....

Q: 1. f(x) = sin 2x + cos 3x + x² = 0 with xo = -0.5 , Ax 0.1, TOL = 0.001, in [-0.5,1] %3D

A: Given equation is fx=0 where f(x) is defined by fx=sin2x+cos3x+x2  Given initial solution is x0=-0.5…

Q: Sx' cos(x4) dx = o 1 cos(x*) + c 4 - -1 - cos(x*)+ c 4 1 sin(x*) + c 4 -1 sin(x*) + c 4

A: *concept :- let, x^4 = t then integrate the simplified term cos(t).

Q: What is the particular solution of the function 3e" sin 5x – cos 5x? A cos 5æ + Bsin 5x + C'e" cos…

A:

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)…

A:

Q: f(x)=X +Sin -1 く(-2)- 4-て+Sini-て)-\no9651 3(x)=てメ+ cosx ずし-て) ニ -4ACOS(-て)-3 (x)-2-らinx f(-2):…

A:

Q: If y = cos x + sin 2x, find the value of y" - y + 3) O 2 cos x + sin x – 2 cos 2x – sin 2x O 2 cos x…

A: Given that: y=cosx+sin2x

Q: 7. y = tan³ (2³) (A) 3x² sec(2³) tan(x³) (B)-3x2 sec(³) tan(x³) 8. y = cos(5x) (A) sin(5x) (B)-5…

A: Topic = Derivative As per guidelines, At a time only three sub-parts of a question can be answered.

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…

A:

Q: 8. f(x) = 2sin² 3x a. 12cos(3x)sin(3x) b. -12cos(3x)sin(3x) c. 12sin(9x)cos(3x) 9. f(x) = 3 cos² a.…

A:

Q: 1. ƒ(x)=x²- = x² - secx 2. w = ex²-x² + 4x 3. h(z)=In(2z)sin(2z) 3x² 4. y= √x² +1 5. y³ + 2xy = 3

A:

Q: 1. * Sx² sin 2x dx -x²cos2x ¸ x sin 2x , cos 2x +C 8. –x²cos2x x sin 2x , cos 2x + C A 2 2 B…

A: To Find : ∫x2sin(2x)dx

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 dx ar and simplify the result whenever possible *+ sin2x sin' 5x 1. y = 2. y sin5x 3. y sin? 4x…

A: Given  The equation is y=-35cot5x3+cot3x3-3cotx3-x

Q: „In sec²(sin2y)dy can be evaluated by writing it as sec2y A sec²(sin2y) - cos2ydy None © In…

A:

Q: V = πT -0.5x Sin 4x 4 +8x-cos2x 2 - X²-4 2²- 19.5x 1.478 -1-082

A: To determine the limit of the following equation.V=π-0.5×sin 4x4+8×-cos…

Q: cOs x dx |(sin? z + 4)%/2 1 sin x sin x cos x 1 cos x +c +c 16 vsin ²x + 4 48(Vsin ²x + 4 16 Vsin 4x…

A:

Q: Find !V1-cos xdx 2 sin x = 1- COS X V2(-cos x/2)+ c 1/ /2(-cos x/2)+ c В. 2/2(-cos x/2)+ c С.…

A:

Q: Sešx cos 8x dx 3x [8 sin 8x - 3 cos 8x] + C A) 73 B) 73 [8 sin 8x + 3 cos 8x] + C C) (8 e3x sin 8x +…

A: MULTIPLE QUESTIONS:   “Since you have asked multiple questions, we will solve the first question for…

Q: If e 17/2- 2i =sin2 then z = %3D - 2i In(sin2) + 4kn -2 In(sin2) + 4kT - 2i In(sin2) – 4kn 2i…

A: Concept : eiθ =cos(θ)+i sin(θ)                  if θ=2kπ                    ei2kπ =cos(2kπ)+i…

Q: tan 2x – 1 dx. 5 tan 2x + 5 Q5: Determine 1 In |sin 2x + cos 2x| + C 10 A 1 В In |sin x + cos x| +C…

A:

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: 23. fx² sin 2x dx is a. b. x² cos 2x -x sin 2x-cos 2x + C x² cos 2x -x sin 2x + cos2x + C -x² cos 2x…

A: Given problem:-  ∫x2 sin(2x) dx

Q: 32. a. b. f cos(4sinx - 1) cos(2sinx + 8) cosx dx is sin(6sinx + 7) − sin(−2sinx + 9) + C 1 1 12. 1…

A:

Q: 2. The suitable Trignometric substitution that solves fx(x-2) dx is (x-1)=sin 0 x-1)3sec0 (x-1)=tan…

A: We can find the answer as below.

Q: 3. = Cos xsin +xax+a 5/2 3/2 1. Ans: Y= 4sin'x* sinx+ To CAx+4)^- Cax+a) 3.

A: To solve: dydx=cos3x sin2x+x2x+1 Solution Given differential equation can be written as: dy=cos3x…

Q: y''-4y'+20y=x^2e^(-2x)sin(4x)-3cos(4x)-xe^(-2x)

A:

Q: Find the iterative scheme for the root of equation sin x-3x +1=0 by Newton-Raphson method. O a. None…

A:

Q: 19. -π/2 21. -π/4 23. [³5e* dx sin 0 de cos x dx sec² 0 do (2x secx tan x) dx 20. rπ/3 22. 24. [¹-dx

A:

Q: sin(6x) cos(4x) dx = sin (2x) sin (6x) (b) 글(s сов (2х) cos (6x) 2 o+( cos (2x) cos (10x) sin (2x)…

A:

Q: Verify y = 4 cos(2x) + 6 sin(2x) is a solution to y" = -4y.

A:

Q: 2x 2)/3x* 2) [3x* - 9x² +1 V9-x² dx .2 3) [ sin xcosx dx x cos.x 4) S sin² xcos 4) sin x cos x dx

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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 -…

A:

Q: If y= x2 sin 2x, then y = А) 2х cos 2x B 2x (sin 2x - x cos 2x) C 2x (sin 2x + x cos 2x) (D) 4x cos…

A:

Q: 1. Evaluate f sin*(2x + 3)cos (2x + 3) dx sin(2x + 3) put = t 2. Evaluate f dx Put x2 + 5 = t x2+5…

A: Explanation of the solution is given below.....

Q: sin(4x) cos (2x) dx = +(st)(9) (e) None sin sin (con (2x) Cos сов (10х) sin (2x) sin (10x) (e)( (Cо…

A:

Q: 1. f(x) = 2x² – 3x + 4 2. f(x) = e-2x sin 5x 3. f(x) = x cos7 x 4. f(x) = 5 sin 3x – 17e-2x cos 3x…

A:

Q: 6 (A) /₁ √== B)/ -x/4 D) dx = tan* (x) sec²(x) dx = C) [rea *² x² ex dx = E) 2x cosh(x²) dx = F) /…

A: Since you have posted multiple questions. As per guidelines we"ll solve only first question. If you…

Q: (2 - 3 sin 30 + y) dy- (9y cos 3p- p+1) do 0, y (0) = 2 Dy+4y-6y sin 3p+ q-20= 12 O y-y+9y cos 30- p…

A: We have to find

Q: [² 11. [(2 sinx+cos.x) dx 9. 13. 15. x¹/3 19. 21. 3 x2/3 - dx 17. [(3 cos x - 2) dx [(5x- 2²/1) dx…

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

Q: y"+4y=sin 2x, where y(0)=3 and y'(0)=¾

A:

Q: (9) Verify that yp = sin 2x is a solution of y" – y = -5 sin 2x and use it to find the general…

A:

Q: solve it 1- cos x 37. 1+ cos x 3 38. sin x = cos 2x 39. tan'x + tan?x – 3 tan x – 3 = 0 40. cos 2x…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: n3xcsC3X)ax 3. S sin2xcsc3x+cos²xcsc3x

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…