1 2 = 3. х — 1 x + 1

Q: 18. Solve x?y" + xy' +y = In(x),(x > 0

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Q: 2π 6 11. 3r2 sin e drd0 0 0

A:

Q: H(x)= In(x+2)

A: our objective is to find x

Q: S =m sin(3x)cos(5x)sin(7x) dx: (sin(5x)sin(9x) +sin(x)- 15 sin(15x) +C (लड 4 Select one: True False

A: Let's find.

Q: verify the given equation. 16.∞∑n=0an(x−1)n+1=∞∑n=1an−1(x−1)n

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Q: "/4 4 12. r² sin 0 cos 0 drd0 0 0

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Q: • 7/2 47. cos xdx + – cos xdx = 2

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Q: (-1) A B then A+B = dr (x – 2)(x + 7) %3D 2 I+7' О 1 O 7 O 9 O 2

A:

Q: 14. y" – 4y' = -4te“, Yo = 0, yo = 1 26. y" +2y' + 10y = -6e¬' sin 3t, Yo = 0, yo = 1

A: 14. The given differential equation is, y''-4y'=-4te2twhere y0=0 , y0'=1 Take the Laplace Transform…

Q: s [5xt° 1 7 + 1-9х 13) dx e6x+5 + 4 sin(8x + - - - 5 2 Vx3

A:

Q: 19 · sin 0 = 5 -4 7t 7n 11n B) {", Ila, 6. 6.

A: Given that, -4 - 25 · sin θ = -19    5   - 25 · sin θ=-19    5 +4-25 · sinθ=-19+205sin θ=15·-52sin…

Q: 7. S. 5x4x² 3 sin 2x y = 2 y = 4

A: Solution ) y = 25x .34x^2 Take log both side  log y = log ( 25x .34x^2 )  [ log m.n = log m + log n…

Q: -5 6 3)If So √3x+1 dx then the solution is: 10 O 12 O 16 O

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Q: 9) 5olve For OLO<2M Cose+sin A =1 2.

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Q: Find the general solution of the ODE. y" +9y = 6 cot²3x

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Q: 1. S(Vz5 + Vx ) de с 6 x2/7 +- 2. x5/6 +x³ +C 1 x3 + C 1 7/2 x3 + C х6/5 + - х3 + C + - O A О в O c…

A:

Q: 8. 2/3 cos¹/3 sin dt 0

A: The given integral is;  Cos4/3(t/2) Sin(t/2), limit from 0 to 2pi/3.

Q: と以 196o63 : A-zi+6j 真京-1AHBIhose Ju+36+9 = XA XB + YAYB+ ZA- ZB 下R-12+4+t(o +-34) 2-6-32AR 長ね4 -7 ら…

A:

Q: You are given that so(x)=e" – 0.001z² for x > 0 Calculate 5|15q65

A: Given that, s0x=e-0.001x2  for x≥0

Q: Find the following indefinite integral.

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Q: S find L-1 cot-12 k

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Q: [6.6] Find dy for the given values of x and Ax. 56) y = x3 + 2x; x= 2, Ax = 0.01

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Q: O cos Z 12 15

A: Right angle triangle

Q: 1/2 S x²√1-x²dx. 0

A:

Q: 3) Solve For OsO<2M VZ COS O + 2öin20=sin 20

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Q: 7. | (32+2) sin(z) dz Bz+

A: 7)

Q: .3 29. dr 18 31. 1/2 sin (x/2 + 1) d

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Q: 12 17 Find p, q if s" f(x) dx + fi2 f(x) dx = " f(x) dx. (Give your answers as whole or exact…

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Q: 38) - con A) 0 sec B) 5π T, 13л 5т D) 0 3 12 12

A: Find the value of x which satisfy sec(x/2)=cos(x/2)

Q: 1. Determine the possible value(s) of x. 12х — 35

A: The figure is

Q: 器+7+6= Stn(x + 2y) Sin(x + 2y) %3D

A:

Q: 43. If |2| > 2, then f - dr r = fcos(5) + k B sin-'(5) + k: cosh-" (5) + k: Itanh-"(4)+k B 2

A: by using hyperbolic Trigonometry substitution

Q: у 3 Сі сos 2х + с2 sin 2x y = cqe2* + c2xe²2x

A: See the details solution in below

Q: = -21n|1-√√x-2√√x+C - dx = Statement 1: 1 Statement 2: S √ √ 171- -√x (A) Both statements are true.…

A:

Q: 17. Find all values of where x? – 6xy+ 8y² = 0, and x # 0.

A: we have x2-6xy+8y2=0, and x≠0 Now,  x2-6xy+8y2=0x2-2xy-4xy+8y2=0xx-2y-4yx-2y=0x-2yx-4y=0

Q: d. q(x) = cot-1 ( ) 1-nx

A: Follow the procedure given below.

Q: Evaluate the integrals

A: Since, our aim is to evaluate ∫0π2 5(sin x)32 cos x dx.

Q: 7/4 *(1 – sin 2t)3/2 cos 2t dt

A:

Q: 5. Solve the problem kuxx = xt, u(x,0) = 0, u₁(x,0) = e, Utt - kuxx -∞ 0 ∞ < x < ∞ ∞<x<∞ -

A: Given is the pde. The objective is to find the solution. The solution is for this type of pde is…

Q: az az and ду Ql:- Find the if Z = x4 sin x y³. Əx

A:

Q: 2 7 4 is S cos' xsin xdx 비

A: See the details solution in below

Q: Question 21 Evaluate: J(3x + 1) d. S(3x+1)°d_

A: ∫3x+12dx

Q: 3. Calculate S x²sin(x³ + 1)dx.

A:

Q: S(32+2*)sin(z)dz 3z +

A: In this question we have to solve Integration.

Q: Evaluate L{cos (3+2t) } scos3 + 2sin3 A s2+4 scos3 – 2sin3 B s2+4 (s+3)2+4 (s+3) 2–4

A:

Q: 26. /(х, у) — х 27. f(х, у) — sin y 28. /(х, у) — х1 + 9у2

A: fx,y=x fx,y=siny fx,y=x2+9y2

Q: 2 35 sint x cos³x «

A:

Q: of dr? e-ex

A:

Q: 0 1 0 0 -4 4 8. 2. D = -1 -1 -3 0. 0. 0. Z = 0 0 0 . 0 0 0 0 . 26. BA 30. AZ 27. CD 31. AI 25. AB…

A:

Q: 4 6 (1+ tan? z) dr = 0.

A: Use identity then solve