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 (2n+1).(2n+1)! (c) E(-1)". (d) E(-1)". 22n-1 n=1 (2n– 1).(2n– 1)! n=1 2n (e) 2 n.n! n=1

Q: | (5e" + 4x° + 6 cos x)dx O 5e + x4 + 6 sin x + c O et – x4 + cos x + c - O 5e" + x4 – 6 sin æ + c O…

A:

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

A: We have, ∫02sinx-xxdx   It is known that, sinx =x-x33!+x55!-x77!+...

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

A:

Q: 10 - cln(2n) e cos (e") dx 0. a) О sin (1) b) O e2m - 1 c) O 1 d) O e27 e) sin (1)

A:

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

A:

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

A: Given, I=∫02cosx-1xdx I=∫02cosxx-∫021xdx now solve both integral…

Q: In y - e* + 2cos z = -3 In y +3cos z = 4- 2e* 2) e2x 1 +3 = +ln(z ex cos z +

A:

Q: SIn(x + 12)dx = O A. (x+12)In(x+12)23-23x +C B. (x+12) In(x+ 12)- 23x +C OCxIn(x+ 12) -x+ C 23 23 +C…

A: We will use integration by parts to solve this

Q: 2x dx (x-1)2 A 2 In Ix-11+C C In Ix-11+C D 2 In Ix-11 +C X-1 2 2 In Lx-11 + + C X-1 O E None of the…

A:

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

A:

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.

Q: cos 2x dx is (sin x+cos x) -1 A. sin x+ cos.x +C B. log sin.x+ cos.x +C C. log|sin.x-cos x| +C 1 D.…

A:

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

A:

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

A: ∫02sin x-xxdx

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: d sin x 1 dt| = dx et + 5 cO X 1 1 1 (A) esinx + 5 (B) e* + 5 (C) (esinx + 5) cos x (D) e sin x

A: We know that integration power rule is given as - Integration of xn is nxn-1.   Here i attached the…

Q: e) S̟ =Č(-1)" sin³(;+n£) Vn+1 n=0

A: The solution are next step

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)…

A:

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

A:

Q: 6) f(x) =xcos x 2n(-1)" • sin(nx) (n-1)(n+1)

A:

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: 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…

A:

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

A:

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

A:

Q: dy 1 dx 3 1 -sin x 3. Find the general solution of +cos(x)y = -e"sinny-². +-cos(x)y 3

A:

Q: e* sin(e^)ax 8+cos²(e*) (x+2)dx x2-3x+5 .2 dx

A: Given that

Q: .1 Find the value of dz and 8z/ dy at the point A when x changes by (0.01) and y changes by (-0.01)…

A:

Q: e) S„ =E(-1)". sin (5 +n5) Vn+1 e) S. = n=0

A: Note:-  Sum of convergent and divergent series is divergent. cos2x=1-2sin2x⇒sin2x==121-cos2xput…

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

A:

Q: 1. (6x + f²)dx + f(2x – 3f)df = 0 2. (cos2f – 3x²f?)dx = (-cos2f + 2x sin2f + 2x³f)df 3. (fe*f –…

A:

Q: sin x - dx 3 ? 22n (a) (-)". 22n+2 (2n).(2n)! (b) E(-1)" (2n +2).(2n + 2)! n=1 n=l 22n+1 8. 22n-1…

A:

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 +…

A:

Q: sin x – x dx = ? %3D 22n (a) E(-1)". 22n+2 (2n + 2).(2n+ 2)! (2n).(2n)! (b) E(-1)"- n=1 n=1 22n+1…

A: ∫02sin x-xxdx

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

A:

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…

A:

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

A:

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: n+2 4) E ' 2x cos(3x + n)dx Ans.

A:

Q: n/10 n/4 (1 + sin x)dx cos? x 1. 2. V1 + cos 5x dx (х - 3)dx x2-6x + 10 dx 2 4. 3.

A: Acc. to Bartleby guidelines, I am solving only 3 parts .  If you want more to be solved ,then upload…

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: 13) y = 4c°(sin 0 – cos ) A) 8e® sin e B) 0 ) 4e0(sin e – cos e) + 4e® D) 8e®(sin 0 – cos 0) 14) y =…

A:

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: 4 E(-1)" sin n=1

A:

Q: sin x - x dx ? %3D 22n (a) (-1)" (b) (-1)". 22n+2 (2n + 2).(2n + 2)! (2n).(2n)! n=l n=1 00 22n+1…

A: Consider the given information: To evaluate the integral ∫02sinx-xxdx

Q: R/2 2 – sin x log + el« dx 2 + sin x/ -n/2

A: Given intergral  I=∫-π/2π/2 log2-sinx2+sinx+exdx

Q: s-4 s+1 2. L(sin 2x + e2x+3) = . s²+4 s-2 Hint: e²x+3 = (e2x)(e³) -7s*+2s²+24 3. L(x* + x² – 7)

A: L{ eat}  = 1s-a    ,  L{sinat} = as2 + a2,     L{xn} = n!sn+11. L( e4x + e-x + x2  ) =L {e4x} + L{…