4 sin(x) cos(z) + 2 sin(z) – 2cos(z) – 1 = 0 V3sin(2x) = - cos(2r)

Q: sin 3x cos 3x (cos 3x + 1)² dx 19) f 22) fex√3-4e2x dx 20) f ITV In x dx 21) f x√4 lnx-1 23)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

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: 3. cos x +sin x- cos(2x) sin(2x), cos(3x), 4 8. ...

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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: cos x sin* x dx 2. [ cor'x sin'x de 1. 7/4 7/3 3. cos x sin x dx 4. /4 | cos³x sin³ x dx

A: According to our guidelines, we can answer only three subparts of a question. Other parts can be…

Q: + 5x + 6 cos x + 2)dx = e – x + cos a + 2 + c - O 3e* + x³ + 6 cos x + 2x + c 3et + x + 6 sin x + 2x…

A: We need to evaluate the following integral I = ∫3ex+5x4+6cosx+2dx

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: SOLVE THE EQUATIONS

A: Given:

Q: 2. f(x) = -5 cos (x) + 2 3. f(x)= 3 cos 2(x + 1) 4. f(x) = -sin 37 x - 1 PS = DCP= PS= DCP = PS =…

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Q: 5. ( sin (7x) cos'(x) dx sin'(x) dx 6. /2 7. cos'0 de 8. Jo sin (20) de

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Q: s sin² (3x) cos³ (3x) dx Hint: cos²x = 1 - sin² x 07 sin²x = 1 - cos² x

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Q: cos^2ydx+(1+e^-x)sinydy=0

A: The given differential equation is cos2ydx+1+e-xsinydy=0.

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: sin 3x 22. Integrate: JS dx V25-cos² 3x A. -sin-1 (os*) + C 'cos3x' (cos 3x` C. -sin *) + C 15 B.…

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Q: 9) S(x.y) = sin (x-3y) Ans. .-2 sin(x-3y)cos(x-3y). S.--6sin(x-3y)cos(x-3y)

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

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: 1. n! n=0 2. (-1)"x2n (2n)! 3. (-1)"x2n+1 2n + 1 n=0 x2n+1 4. E(-1)"- (2n + 1)! n=0 A. sin(x) B. e*…

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Q: integral (x 2 + 2x ) cos x dx

A: The given integral is ∫x2+2xcosx dx. It is known that ∫udv=uv-∫vdu. Let u=x2+2x   and  dv=cosxdx.…

Q: 5. (sin 0 – 2r cos² 0) dr + r cos 0 (2r sin 0 + 1) d0 = 0

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Q: 1) y = x3 + sin x² + sin-1 5x 2) y = 32x + In (sin x²) + In(sin¯' 5x)

A: some functions are given , we have to find its derivative

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: 4) f(x)=- - T <x< T Ans. 4 cos(x) +cos(2.x) - 4 cos(3x) +... 12

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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)…

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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: (x² +1)Z. tan-1(sin 2x) Q2/ B/Find dy if у 3 dx (x2 +4)3 . sin-32x

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Q: 2+ cos (1 + x»'½) .0.5x dx 22 cos (1+x³/2) V1+0.5 sin x 2,0.5x dx|

A: By using Simpson/Trapoizodal rule.

Q: cos x 3. f sin³x dx (2 + sin?x) + C 3 4. S* x sin 2x dx 1-9x2 5. S sin-1 3x dx + x sin-1 3x + C 3

A: Q - 3

Q: *y=(sin(x)+cos(x))cos(x). dyldx -sin 2(x)+cos*2(x)+2cos(x) -sin 2(x)+cos 2(x)-sin(2x) O

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Q: (3 tanx-2 cos y)sec" xdx + tanxsin yay = 0

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Q: x*sin (2x) dx a. ** cos(2x) – x³ sin(2x) –r² co. 3 x² cos(2x) +x sin(2x) +- cos(2x) + C 4 1 cos(2x)…

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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: 7 sin(x) -dx 2 cos x+5cos(x)– 3 4.

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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 -…

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Q: 3. sin 8x cos 8x dx s 2x sin 2x dx cos

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Q: cos" x dx Cosn-1 x sin x n – 1 + п-2 Cos' x dx n n

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Q: 11. y = x² sin x + 2x cos x – 2 sin x 12. y = x² cos x 2x sin x – 2 cos x - -

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Q: 2y 1 + cos 3x - 4.x + 3y sin 3.r = 0 %3D dr

A: 2y-1x+cos3xdydx+yx2-4x3+3ysin3x=0 Rewrite the above ODE in the form of Mdx+Ndy=0.…

Q: sin 3x dr + 2y cos* 3x dy = 0 COS

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Q: 3 In(1+ V sin²x .limr→0 V1– cos x

A: Consider the given expression. limx→0ln1+sin2x31−cosx Put the limit in the expression.…

Q: cos (5x)cos (3x) dx cosh' (In x) sinh (In x) (A) (8) - (C) 0 (D) 2 1

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Q: 12) f)=sin(x) 0<x<1 Ans. 24 1 (₁ A 7 (1)(3) 1 -cos(2x) +- -cos(4x) (3)(5)

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

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Q: cos x sin x dx 4. sin 2x cos 2x dx 5. cos x sin* x dx 6. sin 3x dx 7. sin³ x cos? x dx 8. 3.

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Q: If e/½i =sin2 then z = - 2i In(sin2) + 4k TI 2i In(sin2) + 4k T - 2i In(sin2) – 4kT -2 In(sin2) + 4k…

A: We will find the solution

Q: Integrate with respect to x: sin(3r) a b 2 cos(4x) cos (2r) (5) f e2x cos² () d 3 cos 3 sin(2a) — е…

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Q: integral cos -1 x dx

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Q: Q-1: Integrate the fraction of functions: 1. f- 14a+1 2. sinx- V(1-x) 2-7x-4x2 dx 3. SE 1-sine dep.…

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Q: (1) ſ [ (x³ + 2 + 7 ) dx (3) cos³x dx (2) √ x³ (2) x3 e3x+1 dx (4) sin x sin 2x dx

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Q: V1+ sin (x5) e-y 2(Vx- 1) f-- cos {sin(2x*)} x-2 x2+3x

A: