211 211 sin mx sin nx dx = 2 [cos(m-n)x- cos(m+n)x]dx 0.

Q: 211 211 2-5 sin mx sin nx dx - % [cos(m-n)x- cos(m+n)x]dx = 0.

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Q: (D² – 5D + 6)y = 15 sin x – 15 cos x - -

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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: 2 6. dx (sin x – cos x)?

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Q: Q3- Find i) S sin3x.cos(-5x)dx

A: We have to evaluate the following integral: int sin 3x . cos (-5x) dx

Q: e) y = In(cos 4 x) f) y = sin² x y = In(cos(e3*)) g)

A: We can solve using first order differentiation (using chain rule)

Q: 211 2E1 sin nx dx | cos nx dx 0, where n integer. 22

A: We have to show that

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

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

Q: a) y = sin x² cos 2x 4.

A: Given: y=sinx2cos2x, y=cos4sec23x We know that ddxuv=vdudx+udvdx…

Q: 211 211 2. sin mx sin nx dx [cos(m-n)x- cos(m+n)x]dx 0. TEMIN

A: The detailed solution is as follows below:

Q: a) (sinx + cos 2x)dx (+1) do b) S dx c) S (x+2)(x2-6x+5) 8 cot(In 8)

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Q: 10. f sin x dx 25+cos²x

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Q: Find: O d: x-6,X-1 dy 3 23=Sin (cos 8x)

A: 1 .y=45x3-6x2+x2-12. y=sin(cos(8x))

Q: Find y' : In(cos² 3x) = e*+y + sin-1 y

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Q: 211 211 sin mx sin nx dx = [cos(m-n)x - cos(m+n)x]dx =0.

A: Trigonometric Definite integration

Q: 211 211 4- Cos nx sin nx dx sin 2nxdr 0.

A: The detailed solution is as follows below:

Q: Number 23

A: we have to find definite intregral of given question

Q: (a) / sin sin(8x) + cos(7.x) dx (b) / (3x – 5 sin dx 2 (c) / cos(3t) + sin(5t) dt

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Q: 211 211 S cosr nx dx= | [cos nx cos nx dx = 0. %3D

A: The detailed solution is as follows below:

Q: 11.) F sin (x)cos²(x)dx 2

A: Note:   As per our company policy we should answer only one question each time, so please repost the…

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: "/2 sin x dx Jn/a V1-2 cos x 4.

A: As per the guidelines  we can answer only one question at a time. If you want to get the answers  of…

Q: 3e" + 3x + 10 cos x + 2)dx .2

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Q: 3) f₁ dx do - cos 0

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

Q: 211 211 I sin nx dx =% [1- cos2nx]dx I1, where n integers.

A: ∫02πsin2(nx)dx=∫02π1-cos 2nx2dxUsed the formula cos 2x=1-2sin2x

Q: 211 211 4- Cos nx sin nx dx sin 2nxdx 0.

A: We know that: Sin 2x = 2sinx.cosx

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: (a) L{t+ sin 4t – e cosh nt} -

A: As per our guidelines, we are supposed to solve only first question.

Q: Evaluate the integrals

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 5. (D² + 16)y = 24 cos 4x – 32 sin 4x

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Q: 8) S dx it sinx + cos x a) in (1 + tan =) + c b) In (i - tan £) + c c) - In (1 + tan x) + o 2 d.)…

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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: d) x In y - 2 cos (4e") = 2 tan (x'y) e) --3x =0

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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: 4. J S (esc²a – co sec 0 tand) d0 - -

A: Explained below...

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

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Q: 7. y" + y = 3 sin(2r) +t cos(2t)

A: The general solution of an ordinary differential equation of the form;…

Q: 3T/2 1|sin(x| dx 01

A: Topic = Integration   using this definationsin x=sin xif 0≤x≤π-sin xif π<x≤2π

Q: 211 2E1 sin nx dx = cos nx dx 0, where n integer.

A: To show that ∫02πsin nx dx= ∫02πcos nx dx=0 Where n is integer.

Q: Integrate x cos(2x^2+7) dx. Select the correct response: O sin (2x^2+ 7) + C

A: Integrate using substitution method.

Q: 1 S (4x4 – e3* + cos(2x) – + 5* ) dx - x-1

A: First you need to go through the formula of calculus. Specially go through the details of the…

Q: (c) So cos(-x)(x²)dx (d) S(3x² – 2x + 1)sin dx

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Q: 5 cos(a) sin (x) dx

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: 211 211 ( cos nx dx= | [cos nx cos nx dx 0.

A: given that                               ∫02πcos2nxdx=∫02πcosnx cosnx dx=0 now,…

Q: E valuate dx 7-3 Sin X +6 Cos X

A: solution.

Q: 1. Evaluate 9/ COS x (a) (1 – x)e dx (b) ,"™ dx p) A-2 sin r -

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Q: 211 211 4- | Cos nx sin nx dx % sin 2nxdx 0.

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Q: sin x dx 1+ cos2 x 31. T/2

A: NOTE: Refresh your page if you can't see any equations. . ................(1) substitute…

Q: (3e + 10 cos(x)) dx ntegral =

A: Integration problem....