7/20 2 cos X 1 dx = ? X 22n+2 22n (a) E(-1)"- (b) E(-1)". (2n).(2n)! (2n + 2).(2n + 2)! n=1 n=1 22n+1 22n-1 (c) E(-1)". (d) E(-1)"- (2n +1).(2n +1)! (2n –1).(2n – 1)! n=1 n=1 2n (e) n.n! n=1 8

Q: Part 1: 1 1. S *(In x)3 dx 2. Se3x cos x dx 3. S(1 + x²)e-*dx 4. So x²e*dx

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Q: (a) In(1– x) +xe? (b) 2х 2x 1-cos(x) (d) V1+x-1 Check and briefly explain how to avoid the loss of…

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Q: 5. eу-2*(1 + x?)dx + сos y dy %3D 0, when x %3D 0, у %3D0 2e2* (сos y - sin y) + еУ(2x? + 2х + 3) %3…

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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: 1 Find the L-1 s(s²+2s+5) Oetsec 2t e-tcsc 2t 으글e-tsin 2t et cos 2t

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Q: 3 1. Determine the order and the degree: sin x () - e* () = xy dx². a. Order – 2; Degree – 3 b.…

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Q: n #1. E(-1)" n = 1 Vn° +2 n cos nT #2. n = 1 2" # 3. E(-1)"(/n+1- /n) n = 1

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Q: 2 sin x - x dx = ? 22n (a) (-1". 22n+2 (b) E(-1)" - (2n).(2n)! (2n + 2).(2n +2)! n=1 n=1 22n+1 8.…

A: Consider the given information: To find the integral ∫02sinx-xxdx. Here option (c) is correct.

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Q: 31. (a) 32. (a) 33. (a) 12x-1| dx √2 + x) dx e* - 1| dx L'i lex -3π/4 (b) cos x dx (b) [*/² | } −…

A: Given: ∫-11ex-1dx

Q: (x²-cos(2x). c. T(x) = x d. T(x) x2. find Q at x = t/4. = 100e-3x + In(4x), k=470, A= 0.01r and x=…

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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: This is an example of an Undamped Forced Oscillation where the phenomenon of Beats Occurs. Find the…

A: Given,              x''+7.84x=2cos(3t),                                 ...(1) and  x(0)=x'(0)=0…

Q: COS X -1 dx = ? X 22n (a) E(-1)" (b) E(-1)" 22n+2 (2n +2).(2n+ 2)! (2n).(2n)! n=1 n=1 22n+1 (c)…

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Q: A B - f sin(1-x) (2 cos(1-x))4 dx (2-sin(1-x)5+C 5 (2-cos(1-x)5+C 5 O A OB O O D OE None of the…

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Q: Evaluate the integrals in Exercises

A: Question 7 - Let the given integral be y - y = ∫lnx-5x-5dx       ............(1)Let,t = lnx-5…

Q: Evaluate D3(sinx – 4e) A cos x-32 ex B -cos x-32 e?x -sin x-32 ex sin x-32 e2x

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Q: 2. xp- X2 a. b. + C с. + C d. None of the above dx 3. x(1+x) In xin (1+x")+C b. xarctan (1+x')+C a.…

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

Q: 3. 4. 5. π X dx sin() co₂ (:) ª 2x - 1 4x1 dx 8. 9. (x-1) √x dx _2_2x dx 10. S√₁-2² a x dx

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Q: 1847 In x 5)- b) Show that the ode (x + tan-¹ y)dx + y dy = 0 is exact, then find the general…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other questions as…

Q: dx+ 1.5 +§ (5r – 15)cos (5х — 15)сos dx COS 1.5 Jo (5x)cos 1.5

A: We have to apply the integral by parts.

Q: Q3) Express cos(x²) as a power series. а) 1. 2! + 6! 4! x10 + 3! x14 +. 7! b) 1– 5! c) 1– x5 x7 + 7!…

A: To express the function cos(x2) as a power series. Here, note that the power series of the function…

Q: | (6e"+6x° +4 cos x + 2)dx = %3D 6e + x° + 4 cos x + 2x + c O e – x° + cos x + 2 + c 6 O e + x° 4…

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Q: 1. Suggest ways to avoid loss of significance in these calculations. (a) √√x4+4-2 (b) ln(x+√x² +1)…

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Q: |x²In x dx %3D 13 x'n x- 19 x² +c -x cos x + sin x + c x'3 Inx - x219+ e

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Q: dx dx Q. 7. Find the Fourier sine series of the function: f(x)=x-3r, for 0<x<T. Q. 8. Find the…

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Q: 15a) n=0 (-1)² 7³² (2n)!9" 2n+1 15b) (−1)" 3+¹ 00 n=0n!5"- 15c) √ x³ sin(x²)dx

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Q: 1. Find the particular solution to y' = 3sin(x) given the general solution is y = C - 3cos(x) and…

A: Topic - differential equations

Q: cos X – 1 dx = ? 22n 22n+2 (2n +2).(2n +2)! (a) E(-1)" (2n).(2n)! (b) E(-1". n=1 n=1 (c) (-1)" 22n+1…

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Q: Find  as a series of ascending powers of (x+1) , up to and including the term (x+1)4 ,an approximate…

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Q: The conversion of cyclobutane (C,H3) to ethylene (CH4) is a first-order reaction. This means that…

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Q: 2. In π 2 π ln - 4 e* cos(ex) dx

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Q: 1. L{e³t+cos 6t - e³t cos 6t}

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Q: for 0 (0° < 0 < 2n) in the equation 2sin e cos e - sin e - 2cos 0 + 1 = 0.

A: Given that, 2sinθcosθ-sinθ-2cosθ+1=0. We know that, sinθ=sinα⇒θ=nπ+-1n+α       α∈-π2,-π2…

Q: 2. Solve the initial value problem f"(x)= 2cosec3xcot3x +5 cos(-x)+3, given Зл = 4 4

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Q: |xV4 - x dx x(x – 1)10 dx 43. 44. /* + 1°d – »° dx (x + 5)(x – 5)'/3 dx (x + 1)²(1 45. 46. |3x*VF +…

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Q: 1- ( 5*-1)d xt (2xy-SinyJelya0

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

Q: - Suppose that for a certain leat-cutter ant colony, the birth rate is modelled by: B(t) = 23,000 –…

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Q: (-1)" (2n+1)! n=0 Σ Given: sin x x² n2n+1 for x E R (-1)"(2n +1) 4" (2n + 1)! Compute the exact…

A: Given: sinx=∑n=0∞-1n2n+1!x2n+1 for x∈ℝTo compute: The sum ∑n=0∞-1n2n+14n2n+1!

Q: 10. Evaluate: e-y ** [In(x + y) - dy dx A. α2 a² [In(2a) – 1⁄In(a) − ³] + Ei(-a) − In(a) – In 2 + 3…

A: To find- Evaluate:  ∫1a∫0xlnx + y - e-yx dy dx

Q: L = {cos² (3t)} L = {e-#£} 1 s2+72 (s+3)³ 1. 2s 2 - 2s2+72 (s+3) 1 2 2s s2+72 (s+3)² 1 + 2s 2s2+72 2…

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Q: 19/20 2 sin x - x dx = ? X 22n (a) (-1)". 22n+2 (2n+2).(2n + 2)! (2n).(2n)! (b) E(-1)". n=1 n=1…

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Q: 2 sin x – x dx = ? 22n (a) E(-1)". 22n+2 (2n).(2n)! (b) E(-1)"- n=1 (2n +2).(2n+2)! n=1 22n+1 (2n…

A: If the integrand has a convergent power series representation, then it can be integrated,…

Q: 5. * S sin(1 – x) (2 – cos(1 – x))* dx A C (2-sin(1-x)5 +C (2-sin(1-x)5 +C+ D. (2-cos(1-x)5 +C…

A: topic - indefinite integral

Q: 2 Solve cos 0 exactly over 0<0< 2n. 2

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Q: 3n 2n n S " S"(sin x + cos y)e? dx dy dz 2n 'n A. 2n(e2n + e3™) в. 2п(е2т — езт) c. 2n(e3™ + e2") D.…

A: Given: I=∫2π3π∫π2π∫0πsinx+cosyezdxdydz   We know that; ∫sinxdx=-cosx+C∫cosxdx=sinx+C∫exdx=ex+C And…

Q: 2 sin x – x dx = ? 22n (a) E(-1)"- 22n+2 (b) E(-1)". (2n).(2n)! (2n+2).(2n+2)! n=1 n=1 22n+1…

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Q: (3e" + 4x° + 6 cos x) dx O 3e* + x4 + 6 cos x +c 3e + x4 – 6 sin x + c et + x4 6 sin x + c O 3et +…

A: To find the integral

Q: Solve the exact differential equation (n у - y sin x- бе)ӑx+(3, + cos x + 5 sec y tanу -бу)dy %3D 0…

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