2. cos(4x) = 1 – 8(sin(x))²(cos(x))²

Q: 4. Show that sin(0 – ø) R2 – 2r R cos(0 – 4) + r² dø = 0. -

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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: 9. 2x + cos x = 0

A: We use intermediate value theorem and rolle theorem to show that the given equation has only one…

Q: 플) - cos X = sin x 2.

A: cos(x-π2)=sin x

Q: 11, 0-20² 2. 3. चं 5. T S cos 2x dx sin(²³) cos²(:-) / dx 2x-1 4x dx dx 6. 7. 8. S [² (x² + 0²³) dx…

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Q: 4sin 5x cos 3x-4cos 5x sin 3x/rom x= 0 to x= 2m

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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: 2. Solve: sin 3x dr + 2y cos 3x dy = 0

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Q: 27 1-COS2X dx |+Cos2X

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Q: 1 - cos 4x 1 + cos x dx

A: The given integral,     ∫1-cos4x1+cosxdx

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: y = In(cos 3x) %3D 1 (- sin 3x)(3) Cos 3x y' %3D y' = 1 (- sin 3x) cos 3x 1 y' = (3) sin 3x %3D -…

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Q: 4. If y3 +x³ = sin y + sin x find. dx 3y²-cosy А. cos x-3x2 3y2-cos y В. - cos x-3x2 cos x-3x2 C.…

A: Given: y3+x3=siny+sinx To find: dydx=?

Q: 15. cos³ 3x 3√√/sin 3x dx

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Q: sin(4x) cos(2.x) dx n (2x) sin (6x) cos (2x) cos 2. ()= 4 'cos (2x) cos (10x sin (2x) trts 10 (e)…

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Q: 1 Evaluate [ (x³ +cos(3x))dx 2

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

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: 4. Evaluate 5 cos x dx 3 v2 sin x – 1

A: To evaluate : ∫π6π3 5 cos x32 sin x - 1 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: 9. If y = costhen the second derivative is 5x 25 Cos, 16 5x 5x sin- 4 d. 25 5x sin- 4 a. 25 b. C -25…

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Q: (11) y" +3y' – 2y = e-2"[(20x + 4) cos 3x + (-32.x + 26) sin 3.x] (12) y" + 9y = sin 3.x + cos 2.x

A: We are entitled to solve only one ques at a time and up to 3 subparts only. Given - y'' + 3y' - 2y =…

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: 4 sin 6x cos 3x dx 1. %3D - 9.

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Q: 1. y = In (3 – 4 cos x) + (4x – 5)5 2. y = x² tan x 3. y = x5 sin2x cos 4x %3D

A: We will answer the first three questions as per our guideline. Please resubmit the other question…

Q: cos(2x) dx 1 In |1 – sin(2x)|+c 2 - 1 – sin(2x)

A: Note: It is assumed that the question is asking to test of the validity of the given equation.   It…

Q: 2. 1- x2dx cos(x + 1) dx 3.

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Q: Find cos(4x) sin(4x) da.. To cos(4x) sin(4x) dx : =

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Q: If x= cos n + cos 2n and y=sin n + sin 2n show that  2xy= sin 2n+2sin 3n+sin 4n

A: See the attachment

Q: 6 Evaluate (a) [ a + (4x-2° dx + (4x-2)* dx (2x-3)2 2x sin (x²+!) cos (x+1) dx

A: AS mentioned by you that "none of these is graded please answer 5. These are practice questions"…

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

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

Q: 5. | sin (Tx) cos (Tx) dx

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Q: cos 4x cos 2.xdx 3.

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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):…

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Q: 1 os( 1 (sin(7z))* =| x)+ cos( x)

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Q: 4 cos () dx 10. x³ sin3

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Q: 7 sin(x) -dx 2 cos x+5cos(x)– 3 4.

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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: 1=[", 64 cos(nx) dx x* -16 -08-

A: We have given integral, I=∫-∞∞64cos(πx)dxx4-16 We need to solve that integral.

Q: For | cos 3x cos 4x dx :

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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…

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Q: (9) ſ cos(x²) 2xdx sin x? + c cos x2 + c Option 1 Option 2 sin 2x + c

A: We will substitute  x2 = t

Q: 35) y = -4 sin x 4+ 2+ 2n -2+ -4-

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Q: 1. sin (3z) cos5(3z)dz

A: Note -  Acc. to Bartleby guidelines, we are supposed to do only one question . If you want more to…

Q: = 2. If y = sin³ (-) cos³ (1) prove that y' = sin² (x) cos(x)

A: Topic = Derivative

Q: 6. S cos 4x cosx dx will yield B.금sin Sx + 등sin 3x +c А. sin 5x + sin 3x + C c. 글cos 5x-글cos 3x + C…

A: Note: As per company policy we should solve only one question. So kindly repost the other questions…

Q: (1) f(x) = sin (5x + 6) (3) f(x) = sin(x-³) (2) f(x) = sin (3x4 + 2) (4) f(x) = cos (4+ 3x)

A: To find f'(x)

Q: Where does the periodic function ƒ(x) = 2e^(sin (x/2)) take on its extreme values and what are these…

A: Given,

Q: 211 3- sin nx dx [1-cos2nx]dx 1t, where n integers.

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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: 16. √(16-9x²) dx 17. dx/ (9x² + 4) 18. sin³ x cos x dx 19. f (secs x) dx/csc x 20. Stan² x dx

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