Prove the following identity sin−1 x = cos−1(1 − 2x2)          x ≥ 0.

Q: 1. Which of the following functions are in L¹? in L²? 1 a. sin x |x|3/2 b. (1+x²)-1/2 x²-1 d. 1 -…

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Q: Evaluate the following integral : 1 ( cosx + | cos x| ) dx

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Q: The suitable substitution to evaluate the integral tan (2x) dx is 4 C cos“(2x)

A: Explanation: Given that, ∫tan52xcos42xdx

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Q: 20.| sin³ }xcos" xdx

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Q: Differentiate the following function COS T 1 (a) sec(x) tan(x) (b) (c) sin (4x° + cos(x))

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Q: If f(x) = 5 sin x + 12 cos z, then %3D f'(x) = f'(2) =

A: The question has been solved in detail in the next step.

Q: Calculate the following indefinite trigonometric integral cos³(x) -dx J sen²(x)

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Q: Evaluate the following integral 2 cos? (4t)dt

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Q: Evaluate the following integral. 3 4 4 cos '3x xp. sin 3x 1 18 4 4 cos '3x dx = V1- sin 3x 18 (Type…

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Q: CO X dx V1 + sin² x

A: Given: I=∫cosx1+sin2xdx Use the substitution method to solve the given integral. Let, t=sinx Now,…

Q: |-e+2 COS X 3 x- Sin x

A: Let,

Q: Prove that sin x can be approximated by x − (x^3/6) within 0.01 on the interval [-1,1].

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Q: Evaluate the integral (cos x - x sin x) dx from x = 1 to 2. O 0.72 O 0.48 O -1.37 O -0.53

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Q: (i)[ cos (5x) sin 5.x dx

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Q: cos 3xdx

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Q: Evaluate the following integral. 1/2 7 sin2x dx /1+ cos x

A: We use Trigonometry identities to solve this integral

Q: cos* xdx

A: Integration

Q: Evaluate the following * S sin(4x) dx O cos(4x)/4+C -4cos(4x) + C O-cos(4x)/4 + C O-4cos(4x) + C

A: We can find the answer as below.

Q: Evaluate the following integral. |5 cos (5x)dx 5 cos (5) dx |(Use C as the arbitrary constant)

A: The integral is given by

Q: If f(x) = sin(cos(2x)), then find f' O-1 O -2 O 1 ||

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Q: 2.Expand the following in powers of x i)√(1 + sinx) ii)e cosx iii) cos x²+

A: Given data:- (i); 1+sinx (ii); excosx (iii); cos-1x2-1x2+1

Q: Answer the following completely. Prove: cos x + sin x sin y = sin(32) cos (2) for all x and y such…

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Q: Evaluate si (z* - tan(z) cos(z) ) dx 2-1

A: To find the integral: ∫11x2-tanxcosxx3-1dx

Q: cos(x) -dx sin (x)

A: Let I =( Integration of cosx/sin2x with respect to x) -----(1)

Q: Evaluate the following integral. 5x cos x dx - 2x

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Q: Evaluate the definite integral. cos(x)dx

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Q: Evaluate the following integral. | e2%cos3x dx

A: LetI=∫ e2xcos3xdxApply integration by…

Q: 2+ sin x dx. 3 - cos x

A: This question is about application integration

Q: +o0 In(tan -1 x) dx 1+x2 1

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Q: Evaluate the following integral

A: Consider the given integral

Q: Evaluate the indefinite integral. | cos(T/x²) x3 xp

A: Given data: The given expression for the integral is ∫cos(π/x2)x3dx.     The given expression can be…

Q: Calculate the following integral: (cos(x)) ·(e***) dx

A: The given integral is, ∫cosx·e4xdx. Let I=∫cosx·e4xdx Use integration by parts and solve the given…

Q: e* (1 + sin x de. nx] Evaluate 1 + cos x

A: I am attaching image so that you understand each and every step.

Q: Evaluate the following integral : cos² x dx x2 + 1 0.

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Q: Evaluate the definite integral. cos(xx) dx

A: We have to evaluate the integral                                                      ∫03cosπxdx

Q: Use the substitution formula to evaluate the integral. 27 3 cos2 x sin x dx 1/3

A: Given that: ∫π/32π3cos2x.sinxdx

Q: 7. Evaluate the following integral: 30 cos (2x) sin2 (2x) dx

A: Given that: ∫30cos3(2x)sin2(2x)dx

Q: 1. Compute the following: f sin²(x) dx

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Q: Evaluate the indefinite integral. cos(8x) -dx 1 + sin²(8x) Answer: +C

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Q: Evaluate the following integral. | e2* cos3x dx

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Q: 5) Determine the following indefinite integral cos (3x) (1 – sin(3x))(2 – sin(3x)) -dx

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Q: Evaluate the following integral. 10 sin x cos x dx 5. 3. 5. 10 sin °x cos °x dx =

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Q: Evaluate the following integral. sin (In x) dx 9x

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Q: O Find the solutions of : 1+sinx=2(cosx)´ in the interval 0<x<2T.

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Q: Evaluate the following integral. 5 1+ cos (4x) dx 4

A: Answer

Q: Evaluate the following integra n/2 sin x Vi+ xp- 1+cos x t/3

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