- y = sin² (-1) y = cos" - y = arctan 0

Q: 2. = COS X- 4. Amplitude= de%3D Equation of mid-line: ent Length of period: Phase Shift:

A: Given:- g(x) = cos(2(x-π/4)) To find  Amplitude Equation of midline  length of period phase shift

Q: 플) - cos X = sin x 2.

A: cos(x-π2)=sin x

Q: 11. y = sin 12. y = cos*(-) 13. y = arccos(-) %3D 14. y = arcsin (- 5

A:

Q: 1 S cos³ 3x sin' 3x dx

A: The given integral is: I=∫cos33xsin43xdx   ...1   We know that; The Power rule: ∫xndx=xn+1n+1+C

Q: · y = sin(cos 3x) – sin x cos 3x

A: Given : Y = sin(cos3x) - sinx.cos3x Let's differentiate:

Q: cos 5x dx 2. S 3 + sin 5x

A:

Q: cos 4x 2 dx sin4x 5.

A:

Q: 1 cos(sec-x) dx 2/V3 xVx²-1

A: Let's find.

Q: Evaluate sin (44°) + cos (29°) using differentials. Refer to special triangles.

A: To evaluate sin44°+cos29∘ using differentials.

Q: 1-cos 3x +C dx 1+ cos 3x 3sin 3x

A:

Q: 9. Sin 2X dx COS 2X

A:

Q: 38. Differentiate y = 2 cos² - a. – sint b. - sin 2t C. - sin - d. sin-

A: Differentiate y=2cos2t2

Q: 15. cos³ 3x 3√√/sin 3x dx

A:

Q: 3- cos nX Sin ux dx

A:

Q: | sin(4z) cos(7z) dz.

A: To find:∫sin4zcos7zdz

Q: y = sin' x- cos 3 – cos' x cos³

A:

Q: /2 sin 2x dx Jo 3+cos (2x)

A:

Q: 1-cosx Sin 2x dx

A: Given:  To Find: To evaluate the given integral.

Q: 15 cos(x) + 4 sec (x)dx

A: 1) I=∫15 cosx+4 sec2xdx =15∫cosx dx+4∫sec2x dx =15 sinx+4 tanx+c   (c- constant if integration)

Q: 3. S sin*2x cos$2x dx

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: symbolnc cos(6x) cos(11x) dx = cos(11) sin(6x) + C ncorrect

A:

Q: 5. | cos(7x)dx

A:

Q: Cos 2x dx ) Sin*2× + 8 1.

A: Given ∫cos2xsin22x+8dx

Q: 1-cos 3x +C 3sin 3x dx 2. 1+ cos 3x

A: We have to prove given integral.

Q: cos(2x) dx 1 In |1 – sin(2x)|+c 2 - 1 – sin(2x)

A: Note: It is assumed that the question is asking to test of the validity of the given equation.   It…

Q: |12 sin(4x) cot(cos(4x)) dx

A:

Q: 18. sin³ x cos x dx

A: Here we will use substitution method for solving this problem

Q: Evaluete " 2X Cos(sin --

A: Use the inverse trigonometric identities and simplify.

Q: | cos²x dx 1- sinx cos-x

A: Given. f(x) = cos2 x/(1-sinx) We need to calculate the indefinite integration of above function

Q: Evaluate the integral.

A:

Q: 4 cos () dx 10. x³ sin3

A:

Q: Cos 4x S cos 2x-sin 2x dx

A: This is a problem related to integration. Based on the general formula and concepts we will answer…

Q: 12) Given y = 2 sin2x Period = b 3D Period = 1-- -1- -2

A: Solution: Give y=2sin2x Now use the form [a sin(bx-c)+d] That implise a=2 and b=2   Period =…

Q: 2 sin(30) cos(30x) dx

A: Given integral is ∫0π2sin30cos30xdx

Q: 8e cos 2x dx csc(x) sec(x)

A:

Q: 4. (e) sinx-cos" xr sinx-

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: 5: - S cos(lnx).dx

A:

Q: cos (3x) · (8 sin (3x) – 1) dx = %3D

A: Given that : The integral is ∫ cos ( 3x ) ( 8 sin ( 3x ) - 1) dx  .

Q: 5) (x3 cos 9x dx

A:

Q: 16. S sin 3x cos 3x(cos 3x+1)² dx

A:

Q: cos(2x) dx 2 (sin(2x)+5)*

A:

Q: 4. Evaluate sin (44°) + + COS (29°) using differentials. Refer to special triangles.

A:

Q: Find:  ∫sin(3x) cos(6x) dx.

A: cos(2u) =2cos2u -1

Q: 8 sin(2x) cos(2x) dx

A: We have to evaluate the given integral

Q: Where does the periodic function ƒ(x) = 2e^(sin (x/2)) take on its extreme values and what are these…

A: Given,

Q: За (cos 4x sin 3x – sin3 x)dx a

A: Given: I=∫a3asin3xcos4x-sin3xdx We know that sinAcosB=sinA+B+sinA-B2…

Q: Find ∫ sin 2x/( 2 + cos x) dx.

A: The integral is ∫sin2x2+cosxdx.

Q: Find ∫sin 5x cos 4x dx.

A: Given, ∫sin5x.cos4xdx

Q: 04.) Show that y = (sin x +cos x) sec x = sec² x

A: Given inequality does not equal. See the attachment