12. By using the trigonometric substitution X = x = ; + sin(0) then the integral S - xp- (3+4x-4x2) 7 will be with respect 0

Q: Match the Integrals on the left side with the appropriate techni Prompts dx 3+5 cos x sec'x dx dx…

A: As per Bartleby guidelines we're supported to answer only first three subparts. Kindly repost rest.

Q: 2. Evaluate the integral ſcos (3x) sin (3x)dx in two ways, one with u = sin(3x) and the other with u…

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Q: 10. Suggest ways to avoid loss of significance in these calculations. (1) Vx² +1-x; (3) sin x- tan…

A: 1 x2+1-x By rationalization  =x2+1-xx2+1+xx2+1+x=x2+1-x2x2+1+x=1x2+1+x Therefore, as x→+∞ there…

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Q: 7. Express the solution of y" + 2y' + 2y = sin (3t) convolution integral (you don't need to evaluate…

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Q: Can i get help step by step with this problem?

A: Recall the following facts.

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A:

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Q: s (e² + 4 cos 8z dz 1+sin 8z,

A: A detailed solution is given below

Q: What substitution should be used to solve the integral x²dx |4+9x² O sin u=3x/2 sec u =2x/3 O sec u…

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Q: Obtain the general solution of the following: 2. -z (2- 2) sec'e 3. xdx + sin () Lydx - xdy]

A: 2. The given equation is  dθdz=z(z-z2)sec2θ This can be written as…

Q: 2. a) Evalute the following improper integrals 6. dx 3 3

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

Q: Write down an explicit solution (involving a definite integral) to the following IVP.  a. y'=…

A: See the solution in the given fig. 1 and fig.2

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); u =

A:

Q: (4)Evaluate the definite integral (a)S(1 + sin x )£x 1/2 (b) [ (2t + cost)dt -*/2 x +1

A: As per the Guidelines, I will answer the first 3 Integrals. For the fourth one please repost the…

Q: 4. Evaluate the definite integral_ TC 3. sin(3t) dt 0.

A: Explained below

Q: For the following integration / sin"(24x) cos(24x)dx what is the suitable substitution? a.…

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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: (2) Compute the following integrals. /4 (a) sin (4r) cos (4.r) dæ. (b) cos(ka)e-lz dx, Hint:…

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Q: 4. Find the Cauchy principal values of the following integral: dx. (x²+1)(x²+2x+2)

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Q: The integral of the given function | sin 9x cos 4x dx is equal. .... 13 cos(5x) — 5 сos(13x) А. + C…

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Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); U =

A:

Q: 2 1 e. Use your answers for parts c and d to estimate -dx using Simpson’s rule with n=8 1+x

A: We have to find the integral by Simpson rule

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A: Have to find the anti derivative of 4x2-5sinx+3x that is have to find the integral

Q: 17. If 4 sin x+3 0 on 0 sx < 211, then x=

A: We have to find x if 4 sin x+3=0 on 0≤x≤2π. Solving the given trigonometric equation, 4 sin x+3=04…

Q: Obtain the General Solution of: (z + 2)* cos yudz - [sin y In(3z 4 6) – d

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Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); u = i

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Q: 1 The approximation of dx by the composite Trapezoidal Rule with n= 2 is +4 O X-

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Q: If the integral of x²dx V(9-x²) (0 – →sin 20) + C. What is 0? - -1 O 3Sin (x) O Cos" (3x) O Cos' ()…

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Q: 36. Sin(xy) + cos(yz) = 1. Compute z and az at P = (2, п/12,4). дх ду

A: Let us consider the given function z=f(x,y) The partial derivative of the function is obtained as…

Q: tanh (22) d) evalvare J seen 2 (2n ) e レッ using a substitution Suitable

A: To evaluate the given integral.

Q: sin ® 3y cos3ydy cos 3y dy

A: We have to find out the integral

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); i 5 .5 и 3

A: The function is given by  fx, y = sin8x-5y The point is x, y = 5, 8 The unit vector is  u = 35i-45j…

Q: Q4. Given that: z = y sin(2x) + (1+x²)e* + cos x tan-1(y* + 1) In(y6 + 137)

A: Given that, z=y sin2x+1+x2ex+cosx tan-1y4+1 lny6+137 ∂z/∂x is the partial derivative of z with…

Q: 2. Evaluate the integral J cos (3x) sin°(3x)dx in two ways, one with u = u = cos(3x). Even though…

A: Given: Apply u-substitution method. Use two methods u=sin(3x)  and u=cos(3x)

Q: Following S sin(A) cos(B) dx = ; f sin(A + B) + sin(A – B), | what is the integral of f sin 5x cos…

A: We have to solve the following

Q: Evaluate the following integral. π/4 1 π/2 SS sin Tx cos y sin 4z dy dx dz 0 0 0

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Q: 3 Q19- if z =- 4x³y sin sin (x³y) əz find əx

A: We want to find partial derivative of the given function.

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); u = (i-)

A:

Q: 6 By separation of variables, Solve the following 5 PDES :- du dt = 2 d24 dx2 © o U (0₂t) =(4,t) U…

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Q: 2. If y = 3 sin(2x + 3) show that y" + 4y = 0

A: Given function is: y=3sin(2x+3) To show y''+4y=0 Finding first derivative of  given function:…

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A:

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A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.