Solve the exact DE (2xy³ + cosx tan y +2 sin x)dx + (3x²y² +sin x sec² y-3 csc y cot y)dy = 0 (1) x²y3 + cos x In (sec y) – 2 cos x + 3 cot y = C (2) x²y³ + sin x tan y – 2 cos x + 3 csc y = C (3) x²y³ + cos x tan y + 2 cos x + 3 csc y = C (4) x²y³ + sin x In(sec y) – 2 cos x – 3 csc y = C

Q: 13. To evaluate f 3cos*x-1 dx. the integrand can be transformed to 1-sin2x a. [(3cos x+ csc²x)dx b.…

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Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

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Q: Use a change of variables or Table toevaluate the following definite integrals.

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Q: B.S(cos x + cos 5x)dx D.S(cos x – cos 5x)dx A.S(sin x + sin 5x)dx C.S(sin x – sin 5x)dx 8. S sec³x…

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Q: Use a change of variables or Table toevaluate the following definite integrals.

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Q: Use a change of variables or Table toevaluate the following definite integrals.

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Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

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Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

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Q: What is the dy/dx of y = 3sin²x cos x ? O 3 sin x(sin²x - 2cos²x) O-3 sin x(sin²x - 2cos²x) O 3 sin…

A: Given: y=3sin2⁡xcos⁡x To find: dydx We know that ddxcosx = -sinx ; ddxsinx = cosx

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: Given:  Calculation:  Let ln(p) = u Differentiate both sides (1/p)dp = du Also the limit of…

Q: 11. Evaluate f- 2 sin 3x dx 4+cos 3x a.) -2 In 14+cos3x| + C b.) 3 In 14+cos3x| + C c.) - In…

A: Solve by integration

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

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Q: Differentiate : a. y= x^2 sinx +sin^2x + cos^2x + tan 2x/sin2x/cos2x b. y= In √x^3

A: a) y=x2sinx+sin2x+cos2x+tan2xsin2xcos2xb) y=lnx3

Q: 1. sin x sin ydx + cos x cos ydy = 0 2. 3 ydx = (3x + 1)dy 3. (х — 2 у)dx + (2х+ у)dy %3D 0

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Q: Find the solution. (y - x- xy cotx) dx + x dy = 0 A) xy sinx = c + sinx - xcosx B) xy cosy = c+ sinx…

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Q: 7. Integrate: S sec? (n²x)dx A. 2n tan n² + C В. x sec2 п2 + С C.금tan(T2x) + C D. x sec nx + C 8.…

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Q: 1. * Sx² sin 2x dx -x²cos2x ¸ x sin 2x , cos 2x +C 8. –x²cos2x x sin 2x , cos 2x + C A 2 2 B…

A: To Find : ∫x2sin(2x)dx

Q: Find , where : = sin (x²) cos (y) COS 6.x sin (a) cos (y) 2.x sin (a) O2.x cos (2) 2r sin (2*) cos…

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Q: 4. y = esec²z (A) sec²rtan resec² z (B)-2 secrtanrx sec²z 5. y= Arccos(x²) 2x (A) √1-2¹ 2x √1-x² (B)…

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Q: Find Domain and Range бяц tue Ⓒsin (x+3) +2y x²+2y 3x + y² 3) 3x + Sin (3x) +2y+Z² Ⓒ x+2y cos2x…

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Q: 1. fcosax tan(sin ax)dx - In |cos(sin ax)|+ c ans : or In |sec(sin ax)| + c 2. Ssin(cos.x)·sin x dx…

A: Here we use the other formulas with the given one and also use substitution.

Q: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: Consider the following integral: ∫0π8cos2xdx Use the following formula to solve above integral:…

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: Consider the following integral: ∫23xx2-13dx Substitute x2-1=u→2xdx=du→xdx=12du in the above…

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: Evaluate ∫2x4x2-1dx          ...(1)

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: Given: ∫x6-3x24x5-xdx

Q: Use Table to evaluate the following definite integrals.

A: The given integral is: ∫0π16sec24x dx From the table given , ∫sec2ax dx =1atanax +C. ∫0π16sec24x…

Q: Use Table to evaluate the following definite integrals.

A: Given: ∫0110xdx

Q: 19. -π/2 21. -π/4 23. [³5e* dx sin 0 de cos x dx sec² 0 do (2x secx tan x) dx 20. rπ/3 22. 24. [¹-dx

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Q: Differentiate: y = In cosh (cos 2) O y' = 6 sin 2z tanh(cos 2z) y' = -6 sin 2a coth(cos 2x) Oy = -6…

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Q: Integrate with respect to x: sin(3x) a b 2 cos(4x) cos (2r) (5) f e2x cos² () d 3 cos 3 sin(2a) — е…

A: We have to solve the following integral .

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: ∫ex3+2exdx Put, 3+2ex=t⇒0+2ex=dtdx⇒2ex dx=dt⇒ex dx=dt2 Therefore,…

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: To evaluate: ∫0π2sin2θ cosθ dθ Solution: Let substitute t=sinθ dtdθ=cosθdt=cosθ dθ Limit will also…

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: Given integral is:

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: Definition used -                 U substitution -                     ∫f(g(x))g'(x)dx =∫f(u)du ,…

Q: Differentiate y= sin'x- cos³x CO A. 3sin x cos x (sinx - cos x) COS B 3sio x cos x (sinx + cos x) C.…

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Q: Use a change of variables or Table toevaluate the following definite integrals.

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Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: To integrate: ∫2x21-4x3dx. Let substitute t=1-4x3. dtdx=-12x2dt-12=x2dx Substituting the value,…

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: The given integral is ∫04p9+p2dp. Let x2=9+p2. This gives  2x dx=2p dpxdx=pdp. when p =0,  x=3. when…

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: To evaluate the given integral, ∫lnπ4lnπ2ewcosewdw. Solution: the integral is ∫lnπ4lnπ2ewcosewdw…

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

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Q: 7.2 (A) 1. S sin x dx cos x + C because(-cos x +C) = %3D dx 2. S cos x dx = because sin x 3. S tan x…

A: We need to solve the given integral. This can be done as follows:

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: Given, The definite integral ∫1249x2+6x+1dx.   To solve: Using change of variables or using table…

Q: Integrate with respect to x: sin(3r) a b 2 cos(4x) cos (2r) (5) f e2x cos² () d 3 cos 3 sin(2a) — е…

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Q: Use a change of variables or Table toevaluate the following definite integrals.

A: The given integral is ∫012x4-x2dx

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: To evaluate the integral: ∫ew36+e2wdw Solution: Let substitute t=ex Differentiating both sides, we…

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: Given     ∫(x+1)42xdx Formula ddx(xn )=nxn-1 ∫xndx=xn+1n+1+C

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: the given integral is: ∫04xx2+1dx we have to use a change of variables or table to evaluate the…

Q: solve it 1- cos x 37. 1+ cos x 3 38. sin x = cos 2x 39. tan'x + tan?x – 3 tan x – 3 = 0 40. cos 2x…

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