1. y=1+sinx 2. y=(1/6)cosx 3. y=cosx+2

Q: find dy/dxy=cosx/1+sinx

A: To find the derivative of the given function y  = cos(x)/(1 + sin(x)).Use the quotient rule for…

Q: L, sin 8x cos 15x dx

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Q: cos 4x 2 dx sin4x 5.

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Q: 5. S(sin3x + cos2x)²dx

A: To find : ∫sin3x+cos2x2dx

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

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

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

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Q: If y=sin(sinx) show that y''+(tan x) y'cos2x=0

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Q: Find. S sin3 2x cos3 2x dx

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Q: 1-cosx Sin 2x dx

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

Q: S16 sin²x cos²x dx ´x cos-x

A: ∫ 16sin2x cos2xdx

Q: 9. S sin(4x – 2) dx

A:

Q: 8. S (1+cos3x)² dx sin23x

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Q: S sin5x cos³x dx

A: Given∫sin5xcos3xdx

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: Evaluete " 2X Cos(sin --

A: Use the inverse trigonometric identities and simplify.

Q: 7. S sin3 4 x cos5 4 xdx

A: To find the integration

Q: Find cos(4x) sin(4x) da.. To cos(4x) sin(4x) dx : =

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Q: Evaluate cos x -2 sinx sin 2x dx Round to 4 decimal places.

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Q: 1- Differentiate. a- Y= 2 ex¹2-1 b- Y= -2 sin³x c- Y= 3sin2x - cos 4x d- tan√(1-x)

A: solution:-(a)  y=2ex2+1dydx=ddx2ex2+1       =2ex2+1ddxx2+1,    chain rule      =2ex2+12x…

Q: 5. | sin (Tx) cos (Tx) dx

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Q: 4 cos () dx 10. x³ sin3

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Q: 6. Find [sinh(4x)sin(2x)dx

A: By using integration by part.

Q: .15 S sin²4y cos>4ydy

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Q: 71. cos³ 2x sin 2x dx

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Q: S sin (3x) 1+cos² (3x) dx

A: Given integral ∫sin(3x)1+cos2(3x)dx The objective is to evaluate the integral.

Q: 6. S cos32x sin*2xdx

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Q: 2 , 1 + sinx +. D. cosx cosx il + sin.x

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Q: ∫cos(15x)cos(4x)dx

A: Integration and differentiation can be considered as inverses of each other. Integration is mainly…

Q: 5) (x3 cos 9x dx

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Q: 4. sin 2x cos 2x dx

A: Here we integrate the given function.

Q: 16. S sin 3x cos 3x(cos 3x+1)² dx

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Q: (9) ſ cos(x²) 2xdx sin x? + c cos x2 + c Option 1 Option 2 sin 2x + c

A: We will substitute  x2 = t

Q: 4. cos 4x cos 2x dx

A: The integration of the integral is cos(4x)cos(2x).

Q: 2. S sin*(2x)cos²(2x) dx 4

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Q: evaluate the integral.

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

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Q: ating / * sin (2x)cos(2x) dr by substitution, if u= sin(2x) th

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Q: Find:  ∫sin(3x) cos(6x) dx.

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

Q: 1. sin (3z) cos5(3z)dz

A: Note -  Acc. to Bartleby guidelines, we are supposed to do only one question . If you want more to…

Q: • TT/3 1– sinx' |dx From right endpoint 1- cscx + n = 4 n/4 coS X

A: We have to find the right end point of the following expression   The given expression is  we…

Q: 2. Differentiate y = /sin(x² + 3)cosx

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

A: We have to evaluate the given integral

Q: 2 2- Find if y = dx sin2x sinx

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Q: 1 dp- sin x cos x cos?,

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Q: S sin(3x)cos(2x)dx

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Q: S sin 3x cos xdx

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Q: If sinx = siny = a and cosx = cosy = b,then cos(x-y) is

A: