Explain Bessel equation and Prove that 2 (n + 4)Jn+4x (i) (ii) In+3X + Jn+5X = 4J"n = Jn-2 – 2Jn + Jn+2 |

Q: 3. The integral of sin24x cos4x dx is a. (1/4) sin³ 4x + C b. (1/3) sin³ 4x +C c. (1/12) sin³ 4x+ C…

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Q: Evaluate the integral: cos 4x cos 6x dx. A) sin 2x + sin 10x + c. 20 -sin 2x + sin 10x + c. C) sin…

A: Let's find integration of given function.

Q: Q1) Express in matrix notation: x' = (cos 2t) x y' = x – (sin 2t)y +1 z' = 1- x + 3y

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Q: 7. Determine the integral| 2+1

A: The given integral,    ∫x dxx2+1

Q: 5. Find the indefinite integral 6.x²dx (2x³ + 7)3/2

A: The solution for the above question is as shown below.

Q: Find the indefinite integral: 10sin 3x - 15 cos 2x + 6 e5x + C O 90sin 3x -60 cos 2x + 150 e5x + C…

A: 30∫cos3x+sin2x+e5xdx=30· ∫cos3xdx+∫sin2xdx+∫ e5xdx=30·…

Q: Calculate the exact value of each definite integral in Exer- cises 47-52 by using properties of…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find the indefinite integral: 30 [cos 3x + sin 2x + e5x]dx 10sin 3x -20 cos 2x +6 e5x + C O 90sin 3x…

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Q: 3dz 1. S 4-5z

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Q: Find the indefinite integral. |cos 2x ein 2* de sin 2x A) 2 +C ein 2x +C B) C) sin 2x e cos2x +C D)…

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Q: Evaluate the Integral 3sin2ß) 4 cos2ß dß. A 30 - (4 – 3sin2f) 5 + C (4- 3cos28) 5+ C B 30 -(4-…

A:

Q: Evaluate the indefinite integral S(z -9-dz 를-9z + 듣 +C 4x4 중-9z + + C 222 - 9x + 7lnx³ + C - 7 9x -…

A: First we write each term using exponent

Q: Find the indefinite integral: O 10sin 3x - 20 cos 2x +6 e5x + C 90sin 3x 60 cos 2x + 150 e5x + C…

A: The objective is to find the indefinite integral.

Q: 8 2 1. Reverse order, then integrate Sr) dydx.

A: Given:    Intergral is given

Q: Evaluate the integral: f sin 7x cos 2x dx. A) sin 5x + sin 9x + c. 2 B) cos 5x +co cos 9x + c. 10 C)…

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Q: Find a general solution of each reducible second-order differ- ential equation y" = 2yy'

A: Recall the chain rule of calculus:

Q: Solve the integral / cos 10x de 1 sin(10x) + C 10 sin(10) + C 1 ·cos(10x) + C 10 1 sin(10x) + C 10…

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Q: EXAMPLE 4 Use the Table of Integrals to find SxVx² + 4x + 11dx. Since the table gives forms…

A: now complete the square ................first answer

Q: Evaluate the integral. Sex. cos 3x dx e2x [ sin 3x + cos 3x] + C O e2x [3 sin 3x + 2 cos 3x] + C 13…

A: Given: ∫e2xcos3x dxe

Q: Evaluate the integral. 7 √49-x² √49-x²-22 49-x² 1 √²-3³ (x² + y² + 2²)1/2 dy dz dx =

A: Solution:-

Q: 2. Use Cauchy's Integral formula, Evaluate the following • I= sin4z ,IZl= 3

A: I am attaching image so that you understand each and every step.

Q: Evaluate Integral. integral 0 to 2 (4/5t^3-3/4t^2+2/5t)dt

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Q: Solve: The integrand (1-cos2 4t) cos4t dt on the integral 0 to pi/12

A: Use Pythagorean identity. 1-cos^2 theta = sin^2 thetahere theta= 4t

Q: Evaluate the integral. 5n /2 2, 1 - cos t dt 3π/2

A: ∫3π25π21-cos2tdt=∫3π25π2sin2tdt=∫3π25π2sintdt=∫3π22π-sintdt+∫2π5π2sintdt=1+1=2

Q: Evaluate the integral. 3x cos 2x dx O e3x [2 sin 2x - 3 cos 2x] + C 13 O 1 [2 e3x sin 2x + 3 cos 2x]…

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Q: Prove using the IVT. ex + In x = 0 has a solution.

A: IVT: If f is continuous on the closed interval [a, b], f(a) ≠ f(b) and k is any number between f(a)…

Q: Evaluate the integral. VZ/2 dr V1-2

A: In this question we have to evaluate the Integral.

Q: Eliminate the arbitrary constants 1. X = -Int, y= at + bt2 2. In y = C, sin ax + C, cos ax + 9x<-2…

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Q: 9 In(z² – 1) dz

A: Given: ∫9lnx2-1dx

Q: Evaluate the integral. 2 Ỉ -1 7t sec ¯¹t dt 2/√√3 2 7t sec¹t dt =

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Q: 10. Using the substitution u 2x - 1, prove that %3D 3 8 dx J1 (2x-1) 25

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Q: Evaluate the integral. Select the correct answer. 1 15 cos ²6 x - = cos 6x + C cos³6 6x- 18 O…

A: Given :∫sin36xdx

Q: Scos cos 3x -1+ cos 5x - dx

A:

Q: ☆ 6. Find the integral of xx²-1 O Sin ¹x + C 4 O Sec-¹x + C Cos ¹x + C Sec-1 (1)

A: Here we have to find the integral.

Q: 4) z = (4 + j3)sinh(3+j)+cos(3-j2)

A:

Q: Evaluate the integral

A: ∫xndx=xn+1n+1+C

Q: 19. Find potential function for = (3xy, æ³)

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Q: Evaluate the integral. '3 4,3 3,2 dt -

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Q: - 2+j= 5 Z153°.435, 3+ j2= V13 Z33°.69, and 1– j2 = /5 2-63°.435 (1 – j2) (-2+ j)(3+ j2) = 1.386…

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Q: How do you integrate z/(z+2) in terms of z?

A: Here, integral is,

Q: Compute cos² x dæ. cos 2x +C 4 cos 2x +C 4 2 sin 2x +C 4 2 O cos cos x +C 3 +

A: Formulae:

Q: 25-28 Use Theorem 5.5.4 and appropriate formulas from geometry to evaluate the integrals. 25. L²₁ (4…

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Q: Find the indefinite integral J(-16r² – 4x + 6)dr. a. -12r-4x + 6r +C b. -4x*- 2r+ áx +c c. -4x-2r+…

A: Solve the following

Q: 3)(2x-ズ) ax

A: First I have split the integral in two parts then just use the rule of integral and find the…

Q: Use the integration theorem to show that Cos nx 효(72-3a2) =D Σ(-1)”-1! -T <x < T n2 n=1 and sin nx…

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

Q: Calculate the given integral: S3 sec“(10x) dx 3) o함n a) O - tan (10x) + 3 tan(10x) + 3x + C 10 1 3…

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Q: Evaluate the integral: –(9z²+7x) dr %3D (1-1)(z+1)²

A: Given :∫-(9x2+7x)(x-1)(x+1)2dx

Q: Show complete solution Expand, that is, perform the indicated operations on the differential…

A: To expand, that is, to perform the indicated operations on the differential operator, xDD+x