|2tan x In (cos x) dx= A sin x [In(cos x)] + C (B cos x [In(cos x)] + C В C [In(sinx)]? + C D -In(cos x)}? + C D

Q: 3. Find the integral (a) f(cos(x) + sin(x))² cos(2x) dx 1/3 /tan(x) (b) dx sin(2x) tan-¹(x) dx (d)…

A: (a)  I=∫cosx+sinx2cos(2x)dx =∫(cos2x+sin2x+2sinxcosx)cos(2x)dx =∫(1+sin2x)cos(2x)dxHere, Let…

Q: Z and dy 없 of y%3 (5x2 - ) (cos ar d²y Determine (cos x + In x).

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Q: e) у- In 2 2xe dx 1 dx xcos(In x) /2 g) y= V1+cos4xdx

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Q: 1. sin x sin ydx + cos x cos ydy = 0 2. 3 ydx = (3x + 1)dy 3. (х — 2 у)dx + (2х+ у)dy %3D 0

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Q: If y = sin(x + 4) cos(7 – x), then is dx A. sin(2r – 3) B. -sin(7–x) cos(x+4) C. cos(2r – 3) D.…

A: We have to find derivative

Q: The f sin x cos x dx is not equal to {A} -cos 2x + C {B} sin²x + C {C}-{cos²x + C {D} sin 2x + C

A: A detailed solution is given below

Q: The f cos 5x cos x dx is 1 {A} = sin 4x - 12 1 1 {B} sin 4x + - 8 12 cos 6x + C cos 6x + C {C} {D}…

A: Given problem:-

Q: 1. * Sx² sin 2x dx -x²cos2x ¸ x sin 2x , cos 2x +C 8. –x²cos2x x sin 2x , cos 2x + C A 2 2 B…

A: To Find : ∫x2sin(2x)dx

Q: Ssint2x)dx = 2cos(2x) (2x) + С -cos(2x) + C O 2 cos(2x) -cos(2x)+ C

A:

Q: y 2sin x-cos 2.x for 0° sxs360

A: Consider the function, y=2sinx-cos2x Differentiate with respect of x,…

Q: 1. If f(x, y)=3x' sin y- y² cos x- 2yln x– xh y- 4xy , find- of ôf ô²ƒ ô²ƒ

A: Given: fx,y=3x3siny-y2cosx-2ylnx-xlny-4xy2

Q: 11 Evaluate (( sin(y²)dydx where 2: 0<y<1, 0<x<y. 0 x a) 1-cos(x) b) 1-cos(x)) 1 - cos() 2 d) 1.…

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Q: 13. Evaluate the indefinite integral fx cos x dx x sin 2x cos 2x a. + c 2 x sin 2x cos 4x b. + c 2 2…

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Q: Solve the DE sinx siny dx + cosx cosy dy - O by separation of variables. A sinx cosy - C sin y B cos…

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Q: 33 Vx2 f(x) = + Ve2x + 2x – In e, x # 1 TT Sin 2x - 1-x

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Q: 21. If y=(x* +sin x)", then dy dx (A) 6(x*+sinx) (4x-cos.x) (B) 6(x*+sinx) (4x' +cosx) (C)…

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Q: 2 sin 2x dx Tcost x + 4 cos² x – 2

A: We will answer the first question since exact one was not specified. Please resubmit the question…

Q: Find the general solution to 2- ди u = xt + x cos t + t sin x. 3 - -

A: Given: 2∂u∂t-3∂u∂x-u=xt+x cos t+t sin x

Q: Find the general solution using Reduction of Order: y''+y'=cos 3x

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Q: 23. fx² sin 2x dx is a. b. x² cos 2x -x sin 2x-cos 2x + C x² cos 2x -x sin 2x + cos2x + C -x² cos 2x…

A: Given problem:-  ∫x2 sin(2x) dx

Q: 2. Evaluate: S(cos x)(In sin x)dx A. sin x (1 – In sin x) + C C. sin x(In sin x – 1)

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Q: Evaluate the integral. (sin Sx cos 5x dx 늘 cos 13x-5 cos 3x + C 26 1 cos 13x - 26 1 sin 13 x + C 26

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Q: Find dy/dx: y = sin (In x²). A 2 cos (In x²) (B) 2 cos (In x²) / x

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Q: dy Find dx е 6х 3 sin (x + 5у) %3D ,6x e O A. 5 cos (x + 5y) 6 e 6x - cos (x + 5y) OB. 5 cos (x +…

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Q: S2ta J 2tan x In (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 cos"() sin(x) dæ cos'4 using the substitution u = 1 = cos(x). | cos"(x) sin(x)…

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Q: Evaluate the integrals using the indicated substitutions.

A: Given: (a) ∫2x x2+123 dx,  u = x2+1(b) ∫ cos3 x·sin x dx,  u = cos x To find: The value of the…

Q: 4) f(x)= cos x COS X %3D (5) f(x)=xsinx -1+ Cos nx

A: Since you post more than one question. As per our guideline we can solve only first question for…

Q: D. 1. If (x + y)² = x² + y² 2. If y = sin³ () cos³ () dy - dx X prove that y' = sin² (x) cos(x) 8…

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Q: Differentiate y= sin'x- cos³x CO A. 3sin x cos x (sinx - cos x) COS B 3sio x cos x (sinx + cos x) C.…

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Q: y" +y' = cos 3x

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Q: (2) Show that y=x sinx is a solution to y"+y= 2 cos x.

A: To Show: y=x sinx is a solution to y''+y=2cosx

Q: If f x?cos x dx = f(x) – S 2xsinx dx, then f(x) is _ A. 2 sin x + 2x cos x + C B. x²sin x + C C. 2x…

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Q: Which of the following is true? A Jsin(3x)cos(4x)dx= [ Sin(7x) – sin(x) Jcos(3x)cos(4x)dx= [cos(x) +…

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Q: Intergrate dy (2y-x) =In Co)

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Q: Compute Cos (x + k ) cos a dx by using substitution technique where k is a constant. [Hint: cos(A±…

A: The given integral is cos(x+k)/cosx.

Q: Use graphs to evaluate 2π S 2r S 0 sin x dx = cos x dx = 2t S 0 2π sin x dx and cos x dx. 0

A: We will find the required.

Q: A Jsin(3x)cos(4x)dx = [ sin(7x) – sin(x). A dx 2 * cos(x) – cos(7x) ® Ssin(3x)sin(4x)dx= [co c) All…

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Q: Integrate with respect to x: sin(3r) a b 2 cos(4x) cos (2r) (5) f e2x cos² () d 3 cos 3 sin(2a) — е…

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Q: 3. f(x,y)= In(x cos y)-cos (In3y)+

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Q: find / sin³ x cos³ x dx cos³ 2x sinº 2x dx 11. 12. cos² x dx sin? x dx 13. 14. 16. 7 sin y dy 7 cos'…

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Q: (1) ſ [ (x³ + 2 + 7 ) dx (3) cos³x dx (2) √ x³ (2) x3 e3x+1 dx (4) sin x sin 2x dx

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Q: The result of solving the integral x' tan(x²) dx is: A) Inlcos(x) +c B) tan(x)-+ In/cos(x²)|+c D) +1

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Q: fip Ify r' sin I, dx a)3x²+ cos x 3. O b) 3x sin x + x° cOS I O cos x 3x sin x + x³ COS 2 Od 13…

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Q: 2tan x In (cos x) dx= A sin x [In(cos x)] + c cos x [In(cos x)] + C © -[In(cos x)]? +C D [In(sinx)]?…

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Q: d'y dy dx² dx 21 29 - -6y=6e¹ cos x; when x=0, 20 dy dx =-629 y = 2e-3x - 2e²x 3e-* 29 (3 sin x - 7…

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Q: on the right. Prompts Submitted Answers D Ssin(3x)sin(4x)dx S(cos(x) - cos(7x)dx} Jsin(3x)cos(4x)dx…

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Q: 6 The coefficient of sin( 2r) in the antiderivative of F(x): F(x) = (cos( is

A: We have to find the coefficient of sin 2x.