Evaluate So sin(x) dx 1+sin(x) 2 Select one: O 1+ 2 2 -1-5 -1+5 2 2

Q: Evaluate sin x dx 1.) S 5-cos x

A: Given that the integral  I=∫sin x5 - cos2 xdx To evaluate the integral

Q: sin x dx 4 3 Show that -

A: The integration can be written as;

Q: Evaluate [/3 cos(x) In (sin(x)) dx T1/6

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Q: y = ce2x cos 3x + c2e2x sin 3x

A: By Bartleby policy I have to solve only first one as these are all unrelated & lengthy…

Q: cos 2x he ƒ -dx is 4+sin 2x {A} In|4 + sin 2x| + C {B} In|4 + sin 2x| + C {C}(4+sin 2x)² + C {D} -(4…

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Q: -3x cos 2x da A) - cos 2x - 3x sin 2x + C B) - 2x- sin 2x +C s 2x - sin 3x + C D) - cos 2x - sin 2x…

A: Since you have posted multiple questions . As per the guidelines we will solve the first question…

Q: Find cos (z+2) dx. O-sin (x + 2) +C O sin (x4 + 2) +C O sin (x* + 2) +C sin (2* +2) +C

A: Let's find.

Q: f(x) = (8 sin x + 3 cos x)tan1 -

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Q: r 3n 4 Evaluate sin'x · cos'x dx 5. n /2

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Q: (b) S tan3 x sec² x dx c) S sin³x cos5 x dx

A: The explanation of the solution is :

Q: y f(x)sin2x + g(x)cos %3D x) =tan3x x)% sin3x %3D - r) =cos3r

A: Differential equation: y''+9y=tan (3x)The auxiliary equation is,m2+9=0m=±3iComplementary function…

Q: (d) sec(x) – sec(x) sin²(x) = cos (x)

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Q: Calculate f 6 sinx cos² x dx.

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Q: 57 sin 6 (똥 + 미) =글(c8 )%3D (cos w - V3 sin w) -

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Q: b) sin 3x 3 sin x – 4sin3 x [Hint: sin 3x sin(2x + x)] Prove

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Q: sin (3x+1)dx 4 cos (3x+1) C

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Q: Express sin 20 in terms of x, where x = sin 0. A. sin20 = sin? 0 = x² 2x(1– x² )² C.sin20 =…

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Q: (1+sinx)9 cos x dx , u=1+sinx is The values of a. (1+sinx) 10 + C 10 b. (1+sinx)10+ c 1 (sinx)10+c…

A: Solution: The objective is to find the value of the given integral

Q: (d) (sin(x + cos(2x + 3√)))'

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Q: = (a) Evaluate S cosx sinx V1 – sin4x dx. -

A: Given∫cosxsinx1-sin4xdx

Q: Evaluate 1 dx 3 sin x – 4 cos x -

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Q: Let f(æ) = - 6 sin(x)cos(x). %3D df dx d²f da?

A: Using product rule, (uv)'= u'v + v'u Here we take, u = sinx v = cosx df/dx =(uv)'…

Q: 1. Determine (i) |cos (2x– 7) dx dx (ii) x +9 (ii) dx 4-9x² 2. Determine (sin x cos x dx using (1)…

A: Since, you have posted multiple questions we will only first question with three subparts as per our…

Q: sin²x dx cos x

A: To decompose the given integral we have to use some basic trigonometric formulas.   We know that,…

Q: Find (f-1)(a). f(x) = 4x3 + 4 sin x + 3 cos x, a = 3 (f=1)'(a) = |

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Q: Find the first and second derivatives of r = [3 cos 2t, 3 sin 2t , 4t].

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Q: Evaluate D³(sinx - 4e²x) A -sin x-32e²x B -cos x-32e²x (C) с cos x-32e²x D sin x-32e²x

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Q: Verify the identity. sin(x + y) – sin (x - y) = 2cos.xsiny

A: To verify the identity, sinx+y-sinx-y=2cosxsiny

Q: Consider these two trigonometric functions: f(x) = 3 sin(2x) +4 %3D s(x) - 3 sin(2x- + 4 -

A: f(x)=3sin(2x)+4applying formula of sin2xsin2x=2sinxcosxafter applying sin2x…

Q: i. Jsin xcos 2x - sin 2x cos xdx

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Q: Verify the identity sin t - cos 2t = (2 sin t - 1)(sin t + 1).

A: sin t - cos 2t=(2sin t-1)(sin t +1)Formulascos 2t= 1-2sin2t

Q: (b) 는(cosx)=-sinx (d) VI+ tan x 1+* Q1) Show that: (a) (1+x) =1+6x (e) (V): *- () %3D

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Q: Evaluate x2 dx Select one: on O(sin (2r- 1) + 2(2 (2ain (r) + sin(2si To (stn(2 1I) 2(2r sin(2sin

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Q: .2 1 2x -1 Prove that : sin .2 dx = 72 1+x 1+x?

A: Solution of given question is given step by step

Q: Sih X pronf:, sin1x) cosinx)dx Sin (1-h)X

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Q: Find (f-1)'(a). f(x) = 2x3 + 5 sin(x) + 4 cos(x), a = 4 (F-1'(a) =

A: here we have a=4 so take f(x)=4 and solve for x using the graphing calculator to graph the function…

Q: Evaluate sin z -dx /4 - coS I

A: Use the substitution method and first simplify the integration than integrate.

Q: Evaluate D³(sinx - 4e²x) (A) sin x-32e²x (B) -cos x-32e²x C -sin x-32e²x D cos x-32e²x

A: Finding the third derivative of the function

Q: D Sin 2x 46 4 Sin -3 = -3%3D

A: (a) Given trigonometric equation is: sin 2x = 4 cos 2x We have to find the general solution.…

Q: find δƒ/δx and δƒ/δy. ƒ(x, y) = sin2 (x - 3y)

A: Given: fx,y=sin2x-3y  To find: ∂f∂x,∂f∂y

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

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Q: Q.23) cos Q.24) cos(sin ¹x) = 24 sin11x) √1-1 d)√1-x² b) (sinx+1)+c 11

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Q: fleax s [[e-8x sin(6x)] dx *Using the formula Evaluate ax sin(bx)] dx = 1 (a² + b²) eax [a sin(bx) —…

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Q: dx |2 sin 2 sin x — сoS X

A: I have appended the formula used in the solution part

Q: Find (f-1)'(a). f(x) = 2x3 + 4 sin x + 2 cos x, a = 2 (f=1)'(a) =

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Q: Use the double-angle formula cos 2x = 2 cos x – 1 to evaluate the integral 1 1+ cos 2x dx

A: The given integral is ∫11+cos2xdx

Q: Evaluate D(sinx - 4e2) (A -cos x-32 ex B cos x-32 ex -sin x-32ex sin x-32 ex

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Q: Evaluate: tan(4x +3)dx A 4 A -In |cos (4x + 3)|+c B -In |sin(4x + 3)|+C 1 (c) -In |csc (4x+3)|+C D…

A: Integral calculus is the fundamental discovery was the link that exists between this and the…