2. y = sec- (6a2 –- 3x + 2) 3. y = (8x – 6) sin (8x – 6) 4. y = cos- (8x - 4)

Q: Evaluate [(1 +x-3 + sin4x)dx -2 cos4x X - + c 4 0x-- cos4x + C cos4x O 2x- 4 0 4x-두-5t +c cos5x + c…

A: As we know that the integration of : ∫fx±gxdx=∫fxdx±∫gxdx ∫xndx=xn+1n+1+c ∫sinxdx=-cosx+c

Q: |5sin(4x + 5) sin(2x --) dx

A: We need to evaluate the given integral. We will use the formula  Cos(A+B)-Cos(A-B)=-2 SinA SinB

Q: 5. S(sin3x + cos2x)²dx

A: To find : ∫sin3x+cos2x2dx

Q: 11. cos4x-cos2 dx sin4x-cos2x

A:

Q: 2. tan3x(sec3x – cos3x) dx

A:

Q: 15. 2sin3x + sin²x - 2sinx -1 = 0

A: Given equation, 2sin3x+sin2x-2sinx-1=0

Q: 5х, 5x sin°(cos* () dx 5 4 6 6

A:

Q: sin (2t + 1) - dt cos? (2t + 1) 31.

A: Use trigonometric substitution method for solving the integral.

Q: 3 (4+sin-15x)° dx (8) V1-25x2

A:

Q: 1. [(10 cos2x - 5 csc2x +4 tan2x + 8 sin2x)dx

A: Integration properties help to find the integration of the given function. Integration property for…

Q: 2 3. sin³x cos³x dx OSx Show two solutions. 0.

A: Given  The integration is I=∫0π2sin3x cos3x  dx.

Q: / – 9x* sin²(7y") = 9x* cos²(7y/") What is y(4) if y(0) = 8? %3D %3D

A:

Q: (2.) (1-(In))^ (3.) yn + sin ()

A:

Q: cos(2x) dx 1 In |1 – sin(2x)|+c 2 - 1 – sin(2x)

A: Note: It is assumed that the question is asking to test of the validity of the given equation.   It…

Q: Find all primary solutions of sin(4x)cos(x) - cos(4x)sin(x)=1

A:

Q: 1. cos (- x) - sin (- x) -- sin (주-x) TT =-1

A: Given cosπ4-x-sinπ4-x=-1 We know the identity cos(a)-sin(a)=2sina using this we will get…

Q: Find a particular solution using the Undetermined Coefficients Method of y" -y' + y = 2 sin3x.

A:

Q: If x= cos n + cos 2n and y=sin n + sin 2n show that  2xy= sin 2n+2sin 3n+sin 4n

A: See the attachment

Q: | -3x cos 4x dx A) - 16 3 cos 48 -x sin 4x + C 3 3 3 B) cos 4x -x sin 3x +C 16 3 cos 4x - 16 3 C) -…

A: To evaluate the given intgral.

Q: 2. +4y= sin(3t), y(0)=2, y'(0) = 0

A:

Q: 1- Differentiate. a- Y= 2 ex¹2-1 b- Y= -2 sin³x c- Y= 3sin2x - cos 4x d- tan√(1-x)

A: solution:-(a)  y=2ex2+1dydx=ddx2ex2+1       =2ex2+1ddxx2+1,    chain rule      =2ex2+12x…

Q: 2. Explain why (sinx – 2)(cosx + 2) = 0 has no solutions.

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Q: Verify y = 4 cos(2x) + 6 sin(2x) is a solution to y" = -4y.

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Q: Find sin 2x, cos 2x, and tan2.x if sinx= -- 3 and x terminates in quadrant IV. V13 sin 2x cos 2x tan…

A:

Q: Sz sin2m-10 cos2n-10 —— В (т, п) 2

A: It is known that, βm,n=∫01xm-11-xn-1dx

Q: ( 2 3 2 cos* 3 sin dx O (3/14) cos*7 (2x/3) - (3/10) cos^5 (2x/3) + C O (3/14) sin^7 (2x/3) - (3/10)…

A: Here, we need to find the integral ∫sin323xcos423xdx. So,                ∫sin323xcos423xdxLet…

Q: Solve: sin 3r dr + 2y cos 3r dy = 0 %3D

A: First make the differential equation in seperable variable form, that is taking function of x with…

Q: 4. Find all solutions of sin x+ 2sin x cos x-0 if 0sxS2.

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

Q: 1.) Solve for 0 <x < 2n. 4sin'x - sinx = 0

A: Explanation of the solution is given below....

Q: 2y 1 + cos 3x - 4.x + 3y sin 3.r = 0 %3D dr

A: 2y-1x+cos3xdydx+yx2-4x3+3ysin3x=0 Rewrite the above ODE in the form of Mdx+Ndy=0.…

Q: In(1+cos 3x) +C dx 3. 1+cos 3.x

A: Differentiate of the RHS the we get RHS

Q: 1=[", 64 cos(nx) dx x* -16 -08-

A: We have given integral, I=∫-∞∞64cos(πx)dxx4-16 We need to solve that integral.

Q: 13T (b) sin-(sin(- -)) = %3D 11

A:

Q: 1- cos 4x sec2 2x – 1 = 1+ cos 4x

A: Question is solved.

Q: 2. y= 4sin(2x- T) and y= cos(3x-) 2

A: According to question given that y=4sin2x-πy=cos3x-π2

Q: Find a particular solution using the Undetermined Coefficients Method of y" - y' + y = 2 sin3x.

A:

Q: 6) y = (sin¬1 8t) (sec -1 derive

A: First, we use the product rule

Q: 1- cos 4x 9. sec2 2x – 1 = 1+ cos 4x

A:

Q: Graph y = 4 sin 5x cos 3x - 4 cos 5x sin 3x from x =0 to x = 2p.

A: Given function:                            y = 4 sin 5x cos 3x - 4 cos 5x sin 3x ,   0 ≤x≤2π

Q: if we let u-4x- 1 for the 2 tan(4x-1)-3 cos (4r-1) dx, what will be the resulting integrand? cos…

A: The given integral is  (2tan(4x-1)-3cos2(4x-1))/cos(4x-1).

Q: 2 0 sin 2x dx 3-cos2x

A:

Q: 2. / sin² cos² xdx

A: As per our guideline we are supposed to answer only one question you can repost other in next…

Q: B. - sin3 p cos 3p sin 3p cos 6p – sin 6p cos 6p H. sin 6p - cos 9p - sin 9p K cos 9p sin 9p LL

A:

Q: Evaluate: | tan(4x + 3)dx i -In |cos (4x+3)|+C A COS 4 В 4 - In |sin (4x + 3)|+C In |csc (4x+3)|+C D…

A: Given: ∫tan(4x+3)dx =∫sin(4x+3)cos(4x+3)dx Substitute :…

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

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Q: (yezy cos 2x - 2e sin 2x + 2x) + (rezy cos 2x − 3)y' = 0

A: given differential equation can be written as  (yexycos2x-2exysin2x+2x)dx+(xexycos2x-3)dy=0 ∵dydx=y'…

Q: By using the method of undetermined coefficients, obtain the general solution for у" - 2y' - Зу %3 2…

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Q: 4. Solve for all solutions to sin 3xcos 2x + cos 3x sin 2x =1 on [0, 2

A: Given: sin3xcos2x+cos3xsin2x=1 Identity Used: sinacosb+cosasinb=sina+b

Q: 4x – 1 for the 2 tan(4x-1)-3 cos² (4x-1) dr. what will be the resulting integrand? If we let u =…

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Q: */2 2 cosx dx 1+ (sin x)2 -n/2

A: