211 211 2-5 sin mx sin nx dx - % [cos(m-n)x- cos(m+n)x]dx = 0.

Q: dy y Cos x 2 dx = 2+ tan n %3D Solve COS 2

A:

Q: 211 211 cos nx dx= [cos %3D %3D nx cos nx dx =0.

A:

Q: 1. f(x) = In 5x 2. у %3D 103х Final Answer: Final Answer: 3. y = sin(e3*) 4. y = cos 2x (e*²-1)…

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: 211 211 sin mx sin nx dx = 2 [cos(m-n)x- cos(m+n)x]dx 0.

A:

Q: y" +3y' – 2y = e-2*[(20x + 4) cos 3.x + (-32.x + 26) sin 3.x] |

A:

Q: 6. Solve y sin (x) cos (x) with initial condition y'(7) = 1 and y(7) = 0.

A: y = 1/4 [ x - 1/2 sin2x] +x -π/4

Q: z = y sin(2x) + (1 + x²)e* + cos x tan¬(y* + 1) In(y6 + 137)

A: ∂z∂x=∂∂xysin2x+1+x2ex+cosxtan-1y4+1lny6+137=∂∂xysin2x+∂∂x1+x2ex+∂∂xcosxtan-1y4+1lny6+137=2ycos2x+1+x…

Q: 211 2E1 sin nx dx | cos nx dx 0, where n integer. 22

A: We have to show that

Q: 8 sin (2t) + 14 cos (t) = 0 for all solutions 0

A: Given equation 8sin2t+14cost=0Solution :8sin2t+14cost=082sintcost+14cost=0…

Q: 211 211 2. sin mx sin nx dx [cos(m-n)x- cos(m+n)x]dx 0. TEMIN

A: The detailed solution is as follows below:

Q: 11. sin(4x) dx e 0.

A: Given: To evaluate:   The given integral.

Q: 19 18. sin x cos x dx 1-3cos 2x dt 1+ e-t

A: The given integrals are;  19) sinxcosx/(1-3cos2x)  18)1/(1+e-t).

Q: 37/2 8 cos x dx T/2

A:

Q: -2 e* sin(x) -dx 1+ x2

A: the solution is as follow we will solve the given problem by numerical method  Trapezoidal rule

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: (a) e3 sin 2x da sin 2r (b) x* In x d.r (c) sin r cos rdr 3. (6)

A:

Q: 211 211 sin mx sin nx dx = [cos(m-n)x - cos(m+n)x]dx =0.

A: Trigonometric Definite integration

Q: 211 211 4- Cos nx sin nx dx sin 2nxdr 0.

A: The detailed solution is as follows below:

Q: e) S̟ =Č(-1)" sin³(;+n£) Vn+1 n=0

A: The solution are next step

Q: (a) / sin sin(8x) + cos(7.x) dx (b) / (3x – 5 sin dx 2 (c) / cos(3t) + sin(5t) dt

A:

Q: 211 211 S cosr nx dx= | [cos nx cos nx dx = 0. %3D

A: The detailed solution is as follows below:

Q: 3e" + 3x + 10 cos x + 2)dx .2

A:

Q: 3) f₁ dx do - cos 0

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: 211 211 I sin nx dx =% [1- cos2nx]dx I1, where n integers.

A: ∫02πsin2(nx)dx=∫02π1-cos 2nx2dxUsed the formula cos 2x=1-2sin2x

Q: 211 211 4- Cos nx sin nx dx sin 2nxdx 0.

A: We know that: Sin 2x = 2sinx.cosx

Q: -9 4s4+s*V5-6 ds s4 1-cos? x dx sin x 2. 3.

A:

Q: 2ä + 2i + x =1 with x(0) = 0 and ¿(0) = 2 Answer: x(t) = 1+ 3e-0.5t sin 0.5t – e-0.5t cos 0.5t

A:

Q: 2 tan 4x dx The is equal to 1- tan 24x A. In(sec 8x) + C B. In(sec 8x)8 + C 1 C. In(sec 8x) + C D.…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: 7 sin(x) -dx 2 cos x+5cos(x)– 3 4.

A:

Q: 1. S(tan -1) dp 2. sin2 B cos ß dB 3. S: xdx -7-8x-x

A:

Q: 2. In π 2 π ln - 4 e* cos(ex) dx

A:

Q: 1o² (sin x + cos x)dx = O 2 O None O 1

A:

Q: 1. f(x) = In 5x 2. у %3D 103х Final Answer: Final Answer: 3. y = sin(e3×) 4. у %3 cos 2x (e**-1)…

A:

Q: 25. æ sec (a²) tan(æ²) dæ | sin? x dx (Hint : cos (2x) 26. 1 27. dx 4- (ӕ — 1)? 1 dx 9x² + 25 28. dx…

A:

Q: .2n erl4h cos²0 r² dr sin@ d0 ¢ dộ = x 32πα 1 X = ? 0 JO

A:

Q: sin(4x) cos (2x) dx = +(st)(9) (e) None sin sin (con (2x) Cos сов (10х) sin (2x) sin (10x) (e)( (Cо…

A:

Q: 1 dx 3 sin x+4 cos x+3

A:

Q: d) x In y - 2 cos (4e") = 2 tan (x'y) e) --3x =0

A:

Q: 18. S sin xdx 2-cos² X

A: The given integral is: I=∫sinx2-cos2xdx    ...1 As we know the common integral; ∫11-x2dx=sin-1x+C

Q: (a) [In(4) - 2e¹³] dx d b) dx d (c) [2²² - 1 (2²)] = 4e³x In(x [sec (12r) + tan-¹(2x)]

A: NOTE: Refresh your page if you can't see any equations. .

Q: 211 2E1 sin nx dx = cos nx dx 0, where n integer.

A: To show that ∫02πsin nx dx= ∫02πcos nx dx=0 Where n is integer.

Q: 4. S(1 – cos 4u) du 5. S sin x cos x dx

A: 4) Given:        ∫1-cos4udu Apply linearity:    =∫1 du-∫cos4u du     =u-∫cos4u du

Q: 49. * ccunlı * sinh xdr = In 2 e€u«lı * sinh xdx = A. e - e B. c - c C. ei - e В. D. ci - 1

A:

Q: 11.| V1- сos 2x dx COS

A:

Q: 10e²x When x = 0, y = 0, y' = 0 9. (D2+1)y= Ans: y=-2 cos x-4 sin x + 2e2x

A:

Q: 1. (a) Find sin 6x+ cos 4x dx. (b) Evaluate dx. Hence, solve dx. (e' +2) (e'+2)

A:

Q: 211 211 ( cos nx dx= | [cos nx cos nx dx 0.

A: given that                               ∫02πcos2nxdx=∫02πcosnx cosnx dx=0 now,…

Q: Find the General and Particular solution of = 8 sin 4x ; y= 6 when x = 0 dx Find the General and…

A: The given equations,1.dydx=8 sin4x ; y=6 when x=02. dydx=4y ; y=3 when x=0

Q: 211 211 4- | Cos nx sin nx dx % sin 2nxdx 0.

A: