1. S(esin x cos x - acos 2x sin 2x)dx

Q: COS x dx 1+ sin x

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Q: b) S sin 2 x cos x dx

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Q: 8. Evaluate the integral. sin x xp. 4+ cos x

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Q: 13. Find y' for sin(xy²) + x² = y². %3D

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Q: (24) Evaluate the integral: | Va sin(1 + x/2)dx.

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Q: 4sin 5x cos 3x-4cos 5x sin 3x/rom x= 0 to x= 2m

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Q: x sin wx O Show that dx = x² + 6x + 10 (3 sin 3w + cos 3w) w> 0

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Q: 18) e2x = sin(x + 3y)

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Q: 2 a) lím sin x+1

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Q: Prove that x2 cos x dx = T(2 – n) (+ sin æ)?

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Q: Evaluate the integral.  integral sin 9  x cos 3x dx

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Q: Evaluate the integral. ∫0 π/2  Sin2 x Cos 2 x dx

A: Consider the given integral as Use the identity to solve the integral such that

Q: Evaluate the definite integral. sin x dx -dx J12 I+cos² x

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Q: Evaluate the integral.  integral sin 3  x cos 5x dx

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Q: Evaluate the definite integral. 1. S(sin(2x) – cos(2x)) dx

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Q: 4. Evalaute cos(x) sin(x) dx

A: Given:

Q: 11. Evaluate the integral sin(y*) dydx.

A: To solve this Intergration we have to use the concept of change of order of integration.

Q: x4 1 If u = tan(- + y° x² – y² - then show that ди du + Y- ду X - = sin2u dx

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Q: 1(y) = In(sin(cos(y²))) %3D

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Q: Evaluate the integral.  integral sin 9  x cos 5x dx

A: Given :           ∫ sin9 xcos5 xdx

Q: The value of the integral (x–1)* sin (x 1) (x-1) +cos (x-1) is

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Q: Se2* (sin x + cos x)dx

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Q: 2. Evaluate the definite integral f²n 15 sin*(3x) cos(3x) dx

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Q: Evaluate the integral sin x dx (2 + 3 cos x)2

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Q: 9. . 2 CoS cos rsin?x dx. 10. 2 sinºx dx

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Q: ,2x Set* sin(e2*)dx

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Q: (a) Evaluate the integral sin* 4x cos3 4x dx

A: a) Evaluate the integral                                 ∫0π8 sin4 4x cos3 4x dx  Let us substitute…

Q: Show that where n is a positive integer.

A: To show

Q: Evaluate the integral.  integral sin 6  x cos 5x dx

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Q: 2. S sin*xcos³x dx

A: As per guideline we have to solve only one question Since the ist question is incomplete so I have…

Q: 5. Evaluate 1. S, sin(x2) dx

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

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Q: 1 a) 1+ sin(x) xp- Vtan (x)dx

A: a) Given integral is ∫11+sinxdx

Q: (d) ſ tan² 3t dt 5 cos? x – 3 tan x dx - (e) S cOs X

A: The integration of the integrals is d) tan2(3t)  e) (5cos2x-3tanx) /cosx

Q: 18. S sin xdx 2-cos² X

A: The given integral is: I=∫sinx2-cos2xdx    ...1 As we know the common integral; ∫11-x2dx=sin-1x+C

Q: Show that d 1 In cos(x) os(x) - csc(x) dx 1+ cos(x

A: We have to proof

Q: Evaluate integral 0 to pie sin 2 x cos 4 x dx

A: To Evaluate the integral given below:-I=∫0πsin2(x)cos4(x)dx

Q: 4) Evaluate the following sin (x) -dx 1+ cos (x) 1 ex dx (4x³ + 7*)dx --

A: Consider the following integral: I=∫sinx1+cosxdx Substitute 1+cosx=t→-sinxdx=dt→sinxdx=-dt in I:…

Q: S 4 cos (x) sin (x) dx = %3D

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Q: Evaluate the integral.  integral sin 3  x cos 2 x dx

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Q: Evaluate the definite integral. 2/2 5 cos(x) sin(sin(x)) dx

A: Given : Definite integral ∫0π/25 cosxsinsinx dx   To find : Evaluate the given definite integral?

Q: What would be your of 'du' using the IBP (e^x) (sinx )dx * none of the above e^x cos X sin x sin x…

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Q: 9. Evaluate ſ,(cos x – 1) dx. Tt/2 - π/2

A: topic - definite integral

Q: 2 Recall thal cos-x= arccos x, Find /2 X Sin (cos x) dx. C.

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Q: 1 Evaluate the equation /o x² sin (xy)dydx

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Q: dy.xandy in =cos = COS e

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Q: 9. (2 sin x – 3 cos x) dx • T/2 - T/2 -

A: We use Trigonometry table for final answer  and cos(-x) = cos(x)  sin(-x) = -sin(x)

Q: 7. Find (a) y = (x* + 5x) cos 5x %3D dx

A: We can find the derivative using product rule as below

Q: Evaluate the definite integral. 1. 2 cos-¹(x) √1-x² dx

A: Given Problem:- ∫-11-2cos-1x1-x2dx