( sin (In 2x) - cos (in 2x))? +x dx 2x

Q: 2. 1= j tan(4x³) ,sec²(4x²)xdx dx 1- I=31-2x) (In( 5. I= 3. 1= ftan? (3x) sec? (3x)dx

A: Here we have to find the value of the following integrations. Note :   As per our company guidelines…

Q: evaluate using the appropriate method or combination of methods.

A: Use 2sinA*cosB=sin(A+B)+sin(A-B) formula

Q: dx 3 cos x+2 sin x-5

A: This integral can be solved by using the trigonometric formulas of sinx and cosx in terms of…

Q: Integrate: So a sin(x²) dx

A: We have to integrate

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: x sin wx dx x2 + 6x + 10 Show that (2 sin 3w – 3 cos 3w) w > 0 %3D - 2e2w

A:

Q: Evaluate the integral: 2 sin(3x)cos(3x)dx A B 1 4/6 —— 1 wlr 3 1 - wlw

A: Given ∫π3π2sin(3x)cos(3x)dx

Q: Find Y'and y" Y = sin (x²) Y = 2x² cos (x²) 2 y" = ? 2

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

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Q: I Eliminate the arbitrary constants -2x 2X Y = C,e cos 2× + Ge sin 3X

A:

Q: Q Is the equation e + x cos x 2 = 0 has real roots?. -

A: To show there are real roots, just use intermediate value theorem on appropriate interval.

Q: Find the General and Particular solution of = 8 sin 4x ; y = 6 when x = 0 %3D dx

A: Since you have asked multiple questions in a single request, we would be answering only the first…

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

A: Given:

Q: x/2 | (cos(x) + sin(2x)) dx of

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Q: Integrate with respect to x: sin(3r) b 2 cos(4x) cos²(2x) a

A:

Q: 4 sin x dx (1 + cos x)²

A: Here we have to solve the given integration.

Q: S[cos 3(x/3)]dx

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Q: Find the General and Particular solution of = -8 sin 4x ; y = 6 when x = o dx

A: As there are multiple questions, first one is solved here.

Q: 2. 1- x2dx cos(x + 1) dx 3.

A:

Q: S cos^3 (x/3) dx

A: ∫ cos3(x/3) dx ∫ cos(x/3) cos2(x/3) dx  ∫ cos(x/3) (1-sin2(x/3)) dx.         ..(1) (Beacuse…

Q: 2x cos x? dx 1+ sin² x² 8

A:

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

A: Given :           ∫ sin9 xcos5 xdx

Q: F(r) = 5x sin(/2x) – 3 cos(/2x) +xe³r sin(3x) + 2x ?

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Q: 1. [* sin' y cos' ydy 3

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

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Q: Eliminate the arbitrary constant ln y = c, sin 3x + c2 cos 3x + 9x^2 -2

A:

Q: 2 cos(플x-지) =D v2 TO

A: Given trigonometric equation is:  2 cosπ2x-π=2 We have to solve for x.

Q: 2- y = prove that (sin x) = cos x %3D dx

A: Topic:- derivatives

Q: cos 3x b. S; dx = ... 3+15 sin 3x

A: We have to solve the given integral .

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: f(x) = cos (In (3x))

A:

Q: 3. fe2x+Inx² sin x² dx = = 2x -+√e²x cos x² dx

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Q: What substitution should be used to solve the integral O sinu=3x/2 O sec u =2x/3 O sec u =3x/2 O tan…

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Q: Given the integral sin(3x + 5) dx cos(3x + 5)

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Q: - Tt/2 2 cosx dx 1+ (sin x)2 -T/2

A: Using substitution: So the limits of the integration would be given by: And

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

A:

Q: 3. S sin? (2t) cos³ (2t) dt 4. ſ tan³(3x)dx

A:

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

A: a) Given integral is ∫11+sinxdx

Q: ,1 x² - 4x⁹+ A) True B False sin(x) (1+x²)² |dx=0

A:

Q: Which is the derivative of y= sin In(5x +2)? * 5 cos In(5x + 2) In 5 5Cos In (5x+2) 5x+2 O Option 3…

A:

Q: Find this second derivative: dz O 2 cos a? – 4x² - sin x² O 4x² cos x² – 2 sin æ² O 82² (cos z²)…

A: Given : Second derivate of sinx2

Q: +3x2. Find dy/dx if: (y)² = sin5(cos³(- -)) 2 %3D

A: Given: (y)2=sin5cos3x7+3x22 ----(1) To find: dydx Let u=x7+3x22 , v=cos3u w=sin5v Now equation (1)…

Q: find integral 2) S sin?xdx dx cos³x

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Q: Find [(1 - cos² t)dt]. dx A. sin²x B. -sin²x C. 1 - sin²x D. - cos²x

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Q: e3x [7 sin 7x + 3 cos 7x] +C 58

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

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: 3) e4x = sin(3x + 4y)

A:

Q: b) Is S cos4xV2 – sin4x dx (2 – sin4x)³ + C true or false? show me

A: this is false because