2. (sin 0-2r cos 0)dr + r cos 0(2r sin 0 + 1)d0 = 0

Q: COS (+3 O cos x Ocos 2x O sin a Ocos z +x) + cos (-) is equivalent to:

A:

Q: 3. Obtain in two ways the general solution of (r + sine - cose ) dr + r (sine + cose ) de = 0

A: Use substitution method

Q: a 1 - x²) cos(nx) dx F(x 一九 4 sin(nл) — 4nл соs(nл) — 2n²л² sin(n) πη3

A:

Q: cos 2x he ƒ -dx is 4+sin 2x {A} In|4 + sin 2x| + C {B} In|4 + sin 2x| + C {C}(4+sin 2x)² + C {D} -(4…

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Q: 1 - cos 4x 1 + cos x dx

A: The given integral,     ∫1-cos4x1+cosxdx

Q: 1. ) cos (4) COS -π/2 f/² sin (1) sin (²) dx (Consider initially the first 2 terms)

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Q: 5. ( sin (7x) cos'(x) dx sin'(x) dx 6. /2 7. cos'0 de 8. Jo sin (20) de

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Q: f/² sin (1) 4x ; (**) sin (²) COS (²) dx (Consider initially the first 2 terms)

A: ∫vn dv =vn+1n+1+C

Q: 57 sin 6 (똥 + 미) =글(c8 )%3D (cos w - V3 sin w) -

A:

Q: cos

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Q: /2 2 cos x dx 1+ (sin x)² -n/2

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Q: ¥2/3 6. cos'x sin x dx 5.

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Q: 5. (sin 0 – 2r cos² 0) dr + r cos 0 (2r sin 0 + 1) d0 = 0

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Q: 9. Solve for value of x [0, 2 n ] 2 cos x + V3 = 0 а. b. 2 sin 2 x - 1 = 0

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Q: 37. 2(cos x)-/2 sin x dx

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: 3- If a y + sin y + arctan a = sin 1 then what is the value of at (0,1)? dz -2 b)- 1+ cos 1 -1 1 a)…

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Q: 7. S sin3 4 x cos5 4 xdx

A: To find the integration

Q: dr de sin - r- cos + eª cos = 0

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Q: 1. ² sin() cos() sin(x) dx (Consider initially the first 2 terms)

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Q: S cos ( x^3 ) dx = * sin ( x^3) + c 3x^2 sin (x^3 ) + c - sin (x^3 ) + c - 3x^2 sin ( x^3) + c none…

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Q: 2 + 3 sin 2x The value of 3x dx equals 1+ cos 2x

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Q: 1. S 2x sin-1 x² dx. 2. S sin² 20 cos³ 20 d0. 3. S sec? x dx V1-tan?x

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 3. у"-2у'— sin 4x 1 cos 4x 40 1 sin 4x 20 Ans. y= c, + c,e²* + -

A: To find: The general solution of differential equation. Given: The differential equation is…

Q: integral cos^7(4x)

A: To find the integral

Q: 4x /² sin () cos (+) sin (²) dx (Consider initially the first 2 terms) 3

A:

Q: 3 8) 1--sin (2t) = sin' (t) + cos (t) sin(t) + cos(t)

A: Given,            1-12sin2t=sin3t+cos3tsint+cost

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

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Q: 3. Determine a root of the equation sin(x) + 3 cos(x)-2-0 Using the Secant method correct to five…

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Q: 1- cos 2x 2 1+ cos 2x 1 (1- cos? 2x)(1+cos 2x) dx = 8. 8.3.25 sin2 z cos a dx = 1+ 8 dx = cos 2x -…

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Q: 1. Solve the DE: (cos y- cos x)y' +cos y sin 2x = 0

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

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Q: 1. Given x = r2 cos(20) and y = -r² sin(20)

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Q: Solve: sin 3r dr + 2y cos 3r dy = 0 %3D

A: First make the differential equation in seperable variable form, that is taking function of x with…

Q: 4. y = tan(x+ a), 5. y = Aex + Be2x, 6. y = A sin 3x + B cos 3x, ,where A and B are arbitrary…

A: According to bartleby guidelines when student ask multiple subpart question then expert must have to…

Q: 11. y = x² sin x + 2x cos x – 2 sin x 12. y = x² cos x 2x sin x – 2 cos x - -

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Q: 1- cos(0) (d) de sin (0)

A: We have to find integration

Q: $5. (i) show that: sin 0+sin 20 = tan 0 1+cos 0+cos 20 (ii)Find the general solution of the equation…

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Q: 9. y = -sin (3x) 10. y = tan (x - 60) 11. y = cos (x + 30) 12. y = 3 cos (2x)

A: In both cases there is translation of graph.

Q: 1. f cos³ 3x sin¹ 3x dx 2. fcsc4 5x cot4 5x dx 3. ƒ cos³ xdx from a = 0 to b = 2

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Q: f/² sin (3) 4x COS ; (**) sin (*) dx (Consider initially the first 2 terms)

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Q: •π 2 (sin³r)√1 (sin³ x)√1 + cos x dx

A: Given problem:-

Q: ♫♫¹⁄² sin (*) cos (*) sin (²) dx (Consider initially the first 2 terms)

A: Solving the definite integral.

Q: 2 0 sin 2x dx 3-cos2x

A:

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: 1. Integrate using an appropriate method. [2si 2 sin³(r) cos² (r)dr

A: The given integral is: I=∫2sin3xcos2xdx   As we know that; The trigonometric identity; sin2x+cos2x=1…

Q: 7. Over the domain 0s x s2n, the equation cos(x)-sin(x)%3D2 cos(2x) has:

A: We find the solution in the following way by using trig identities.

Q: B. - sin3 p cos 3p sin 3p cos 6p – sin 6p cos 6p H. sin 6p - cos 9p - sin 9p K cos 9p sin 9p LL

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Q: 2. cos(4x) = 1 – 8(sin(x))²(cos(x))²

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Q: * /2 2 sinh (sin 0) cos 0 d0

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Q: Determine the general solution of (cos(x)cos(y)-cot(x))dx=(sin(x)sin(y))dy

A: Given: cos(x)cos(y)-cot(x)dx=sin(x)sin(y)dy