cos(1) dt Using an appropriate substitution, evaluate: [2 + sin(1) ]* ™ 3 A +C [2+ sin(1) ]} B 3[2+ sin(1) ]³ +C +C 3[2+ sin(1)]³ 3 D [2+ sin(1) ]³ +C

Q: Sco The value of cos (x+3) dx with U=x+3 is -cos (x+3) sin(x+3) +C -cos(x)+c

A: The given integral is ∫cosx+3dx.

Q: 8. 9. A) 1−sinx Ĵ (COSX + 1 COS X+X 2(cosx+x)2 E) ·x)³ dx = ? 1+tan²a (2 + tana)² -+C B) +C D)…

A:

Q: 1//2 x8 Evaluate: sin" (1-2x')+ cos" (2axvi-x")} dx. 2x²)+cos* 1-x4 -1/V2

A:

Q: x2 – 1 if æ <1 1 f(x) = T In a a cos 2rx + b sin( 4 In 2 if 1<a < 4 2" – x2 if 4 < x - where a and b…

A: For f(x) to be continuous at x = a : LHL= RHL = Value of the function at x = a

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: sinx S- cos?x+ 6cosx+13 O In cosx+3-Vcos²x+6cosx+13|+C O In cosx+3+/cos²x+6cosx+ 13 O…

A: To find:

Q: (a) f(x) =cos (7æ) cos (Tx) 3

A:

Q: Evaluate D(sinx – 4e2) D³(sinx cos x-32 e В -cos x-32e2 C) -sin x-32 e2x (D sin x-32 ex A

A: The objective is to evaluate, D3sinx-4e2x

Q: If e /2i -sin2 then z = - 2 In(sin2) + 4KTO - 2i In(sin2) – 4kT 2i In(sin2) + 4k TO - 2i In(sin2) +…

A: Given e(-z/2i) = sin2 We need to find z. The solution is given below.

Q: -2 a -1 23 1 b-a 2 1 4 T -cos³x sin ²x 1 -2 - e b+ a e 3-b - 1 2 NO - 1 1 -1 O 2 1 013 4 1 خدم برد…

A:

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

A:

Q: 36. (a) Prove the reduction formula 1 cos"-'x sin x + п S cos"x dx = | cos"-2x dx n n (b) Use part…

A:

Q: f cos(x³) x² dx. O 1 ¹ cos4 + c 4 1 3 sin x²+ C 1 1 ¹ cos4 + c - 4 -3 si sin x³+ C

A:

Q: x2 – 1 - if x <1 x – 1 - f(x) = T In x a cos 2rx + b sin(- 4 In 2 if 1<x < 4 if 4 < x where a and b…

A: Explanation of the answer is as follows

Q: If f(x) = -2[cos (2x)] +5[sin(3x)] is a neither function. Determine value for a and B. a=3 and B=2…

A:

Q: |5x sinx dr = - 5x cosx +5 sinx +c OA. 5x cosr +5 sinr +c В. None 5x cosr - 5 sinx +c OD.

A:

Q: f1(x) = sin(x1) cos(x2), T f2(x, y) = xy, f3(x) = xx¹, € R² x = x, yern XER"

A: Given the following functions                  f1(x)=sin(x1)cos(x2),   x∈ℝ2f2(x, y)=xTy,   x, y∈ℝn…

Q: ƒ cos(x³) x² dx. 1 ¹ cos4 + c 4 1 WIT 3 1 -| sin x³+ C 1 ·cosª + c 4 4 -3 sin x³+ C

A: Topic = Integration

Q: 7. y = cos`x sin'x %3D 3 A. – 4 cos x sin x B. – 2 sin sin 2x 3 2 C.- 4 cos´x + sin' D.- 2 sinx cos…

A:

Q: Using an appropriate substitution, f sin³ (x)cos®(x)dx is equal to: sinx + C sin13x + C 13 sin11x…

A:

Q: sin(8t) -2t O a. r(t) = e cos(8t) +e2t O b. x(t) = e 4t cos(8t) – e t sin(8t) COS O c.(t) = e2t…

A: Given,         dxdt=12x-8y        dydt=16x-4y

Q: 1 sin(2x): -1 sin(2x) 125 %3D (D²-1) True False

A: 1(D2-1)3sin(2x)=1(-22-1)3sin(2x)                             =1(-5)3sin(2x)…

Q: sin ( 27 +1)x Prove that dx =7 for all ne N. Sin x

A:

Q: -(sin³(x) + sin (x³) ) dx A 3sin'x + cos (x³) B 3sin?rcos(x³) + 3xr?cos(x³) © 3sin?x + cos (3x²) D…

A:

Q: A B - f sin(1-x) (2 cos(1-x))4 dx (2-sin(1-x)5+C 5 (2-cos(1-x)5+C 5 O A OB O O D OE None of the…

A:

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

A:

Q: St' sin(2t*)dt (sin(2t*) - 2t*cos (2t*)) + C (sin(2t*)-2t cos (2r*)) +C 14 1 (sin(2t*)-2t cos (2t*))…

A:

Q: 32. a. b. f cos(4sinx - 1) cos(2sinx + 8) cosx dx is sin(6sinx + 7) − sin(−2sinx + 9) + C 1 1 12. 1…

A:

Q: Evaluate D3(sinx – 4e) A cos x-32 ex B -cos x-32 e?x -sin x-32 ex sin x-32 e2x

A:

Q: (-1)° x*1 (2k –1)! 2k-1 k=0 a) sin x b) cosx c) sin x- x d) cosx-1 e) e* ||

A: Given,

Q: Q7: Í sin(3z)cos(4z) dz = a)cos z- cos(72) + C b) -tcus x -os(Ix) + C %3D Qe S sin'x cas d = 2).

A:

Q: 2. L{sin² = nt} 7² a. S³+π²s π² b. 772 2s3-2π²s π² C. 772 2s3+2π²s π² d. S³-π²S

A:

Q: O f (x) = -6 sin(3x + 1) cos(3x + 1)ecos"(3+1)

A:

Q: A/ 10 Evaluate 4/1+ cos 10x dx. A/ 10 4/1+ cos 10x dx =

A:

Q: 8. Solve: a sin() = { b 2 cos(a +) +1=0 on <a << 3 algebraically. on 0<a <10 using technology. %3D

A: 8.a) sinx5=23 on 0&lt;x&lt;10πb) 2cosx+π4+1=0 on π&lt;x&lt;3π

Q: Factor  Cos^4 x + 2 cos^2x + 1

A:

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: (d) r(π/6 + At) - r(π/6) = √3 2 cos At sin Ar-1+(cos Ar i+ At + 2 3√3 2 -sin At 1 3/-)1 2 X

A: We can solve as follows

Q: 3. Show f cos2n Ode 277 sin-n Ꮎ ᏧᎾ = 27 22n 11.1 n = 1, 2, 3,...

A: Using Cauchy integral formula.

Q: 12) f)=sin(x) 0<x<1 Ans. 24 1 (₁ A 7 (1)(3) 1 -cos(2x) +- -cos(4x) (3)(5)

A:

Q: 12. If f(x)=sin(2x+1), then f'(x) is equal to A -2 cos (2x+1). 2 cos(2.x+1). 4 cos(2x+1). C D -4 cos…

A:

Q: xp sin 5x cos 3xt cos 5xsin 3x xp x²+ 2x + 5 EX Find:

A:

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: Evaluate sin (4x + 14) dx cos (4x + 14) Ocos (4x + 14) + C O-cos (4 + 14) + C -cos (4x + 14) +C…

A: Integration

Q: cos 2 dx O 32 -cos -5cos2 ()+7] + c 35 32 35 - cos(4)- 32 -cos) +c O 32 COS +C 스4

A: We have to find integral

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

A:

Q: 1 sin(2x) (D²-1) -1 sin(2x) 125 true False

A:

Q: Write the expression as an algebraic expressionin x for x>0. a.  sec [sin-1 (x/sqroot(x2+9))]

A: Since you have asked  multiple questions in single request  so we  will be answering only first…