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

Q: 3. Solve: cos xdx + ( 1+ | sin ædy = 0 %3D

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Q: 5. Use Newton-Raphson method to find solutions accurate to within 10-2 for x - cos x = 0 on [0,…

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

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A: ∫vn dv =vn+1n+1+C

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A: To evaluate the integral.

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Q: 1. f/² sin () cos (+) sin (²) d dx (Consider initially the first 2 terms)

A: We have to use the formulas for 2sin(A)cos(B)-sin(A+B)+sin(A-B) and 2sin(A)sin(B)=cos(A-B)-cos(A+B).…

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: 7. d. cos 0 cos 20 + sin 0 sin 20 = V3 over 0, 2t)

A: We know the sum identities: sin(a+b) = sina.cosb + cosa.sinb sin(a-b) = sina.cosb – cosa.sinb…

Q: 8. Find all solutions of the equation in the interval [0, 2n) a) sin(x+ t/2) - cos?x = 0

A: The trigonometric equations are:          sinx+π2-cos2x=02cos2x+7sinx=5 The interval for the…

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Q: 2 3. sin³x cos³x dx OSx Show two solutions. 0.

A: Given  The integration is I=∫0π2sin3x cos3x  dx.

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: 7. S sin3 4 x cos5 4 xdx

A: To find the integration

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Q: 11 Evaluate ff sin(y²)dydx where 2: 0<y <1, 0<x<y°. 0x a) 1-cos(x) b) (-cos(x)) --cos(1) d). cos(1)…

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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: 5. Consider the equation: 3x – 2 cos x = 0. Use Newton's method starting with the initial…

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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: 22. y' = 1 + 3y tan x. ANS. 3y cos³ x = c + 3 sin x – sin³ x.

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A: Given

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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: 8) Determine the smallest positive roet of the equation - 0.0i t sin (0.573t) -e

A: To determine the smallest root of the given of the function we will use Newton-Rapson method with…

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: 7 sin(x) -dx 2 cos x+5cos(x)– 3 4.

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

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Q: 9. cos (2t) dt 10. " sin?t cost dt /2 11. sin'x cos?x dx 12. (2 sin0)² d®

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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: 3. x = 2 cos(3t) – 4 sin(3t) and y = 3 tan(6t) at t = 2

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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: 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: 4. Find all solutions to the equation 4sin x cos x = v2 in the interval [0,2]

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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: 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: "+25y 4r sin(51) – 2e" cos(5t)

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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