2.5 1 –dx 1+ sin x – cosx COS X 1

Q: x/4 The definite integral sin24x cos2x dx is equivalent to x/2 1 -sin20 cos20 de A x12 2sin20 cos40…

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Q: F(x) = 1+e siny x %3D -- = -15 e sin4X- se"co54X fca) = fco) = -8 R fくり) = fci-2) = 4.2398 > KMS %3D…

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Q: π/2 cos² x dx

A: This question can be solved using the concept of properties of definite integrals.

Q: S (x cos 2x dx) = Solve the integration 8 sin x + 11 cos x + c %3D II

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Q: 7. The value of A. cosx - C O A O B О с O D dx √(1-x is B. sin '(x)+c C. cosx ' +2¢ D. cosx

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Q: cos 2x 12) S 2cos2x sin x – sin x dx -

A: To integrate:∫cos2x2cos2xsinx-sinxdx Solution: ∫cos2x2cos2xsinx-sinxdx On simplifying further we…

Q: TL 2 Evaluate the integral: sin(3x)cos(3x)dx 3 1 A B C D H|m 3 16 1 3 16

A: To evaluate the integral. Option c is correct.

Q: To evaluate 3cos x=1 dr. the integrand can be transformed to 1-sin2x A.) S(3cos³x + csc?x)dx B.) 3…

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Q: r 3n 4 Evaluate sin'x · cos'x dx 5. n /2

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Q: S sin x (1+ cos x) ecos *dx 2. S csc ³ () do 1.

A: 1) Given:       ∫sinx1+cosxecosx dx Integrate by parts:         ∫fg′=fg-∫f′g here  f=1+cosx→f'=-sinx…

Q: (a) f(t) = sin 2r sin 31 (b) f(1) = sin 2t cos 2t %3D

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Q: f cos(x³) x² dx. O 1 ¹ cos4 + c 4 1 3 sin x²+ C 1 1 ¹ cos4 + c - 4 -3 si sin x³+ C

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Q: Q-1: Integrate each of the following without using trigonometric substitutions (a) S: cos(x) xp-…

A: Integrating each of the following without using trigonometric substitutions

Q: cos2x a) -.dx,b) xe*. dy Į sin2x. [In(sin2x)]² + sin2x 0.

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Q: 2n 3. o (x + cos x) dx

A: Given :

Q: xcosx dc + Cos x da 2.

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Q: sin' y 3 Find the particular solution of xsin?y cos y y' +: 1+In x = 4 :y(e) =

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Q: sin²x dx cos x

A: To decompose the given integral we have to use some basic trigonometric formulas.   We know that,…

Q: 1 y Solve the integral: cos -dy dx - T/2 Jo

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Q: 1 dx x +c, find- dx exactly where c is a constant. 5. If 1+cos x = tan 2 X 3+3 cos 4 n dx tam S c /+…

A: It is given that

Q: (c) The displacement, x, of a particle in simple harmonic motion is given by x = cos(3t) – sin(3t).…

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Q: (x*+2 cos x -1+ 20) = 205) = dx %3D fuse rules)

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Q: S cosx. sin“x. dx = cos³x + C sinx + C O None O sin*x 4 + C

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Q: 4. f cos? 2x 4. cos? 2x sin 2x dx 2 2 5. f sin¹¹ ²3x cos / x 3x dx

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Q: Q7: Í sin(3z)cos(4z) dz = a)cos z- cos(72) + C b) -tcus x -os(Ix) + C %3D Qe S sin'x cas d = 2).

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Q: CoS cos³ 0 5./ d0 1-sin0

A: Given problem:- ∫cos3(θ)/(1-sin(θ)) dθ

Q: A/6 Evaluate the integral 3cos 3t sin 3t dt. A/6 | 3cos 3t sin 3t dt = (Type an exact answer.)

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Q: 2. (a) Show that V3 cos x-sin x COS where 0<x<2r . 2 (b) Using the result in (a), solve the equation…

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Q: 1. Integrate x tan- (x²) dx. x4 + 1 2. (a) Evaluate cos? x sint x dx. (b) Calculate dx. x² – 5x + 6…

A: These are integrals which can be evaluated using standard techniques. The solution typed in LaTeX…

Q: 2 a) ; 1 :+ 5e* dx =? sin? x 1- x2 b) (x² – x + 2)* (2x – 1) dx =? sin 2x c) 5 + sin² x dx =?

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

Q: 3. Solve the ODE using Separation of Variables. y². dy = (y² +1) - sin x dx

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Q: tegral 1 -r³e"la0 cos²e ,² dr sin@d0 ¢ do = x 32πα x = ? %3D

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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…

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Q: sin(x) d Find (S sin (4 t) dt). cos(2)

A: Use the concept of derivative of an Antiderivative.

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

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Q: 1. Solve the linear equations below on the interval 0 < 0 < 2n. Show ALL your work!! 2 cos(2x) =-V3…

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Q: 6secx cos x dx is O a. 6x + c Ob. O b. 6 sec x+ c O C. 6 sin x+c O d. - 6 secx +c

A: Given ∫6secx cosx dx

Q: Test for exactness and find the general solution of: (cos2y – 3x²y²)dx + (cos2y – 2xsin2y – 2x³y)dy…

A: To solve the following differential equation

Q: Q-1: Integrate the fraction of functions: 1. f- 14a+1 2. sinx- V(1-x) 2-7x-4x2 dx 3. SE 1-sine dep.…

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Q: Prove that : n/2 1 dx (a'sin'x + b’cos'x 4a°b³

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Q: (1) Evaluate ædx Hint: Express cos* z in terms of sin z. Then use the substitution u = sin z. Back…

A: We can make it easier for you.

Q: 9. Integrate the following: a) S sin? x cosx dx b) "(1 – cos 2x)/2dx

A: (b) The given integration is: ∫0π1-cos2x32dx To find the value of integration.

Q: r = sin 0 + 2 cos² 0

A: Given

Q: 7/2 d sin dx dx COS

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Q: 5. S sin(3x)dx (a) 3cos(3x)+ C (b) †cos(3x)+ C (c) – 3cos(3x)+ C

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Q: Find the general solution separable equathon. t) 2casx cosy dx-3 sinx sinydy = 0 o the given…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…