cos (3z) + sin(3z) c: |2| = 2 to be -dz: Calculate the integral value. 23 (Complex functions theory)

Q: F(x) = 1+e siny x %3D -- = -15 e sin4X- se"co54X fca) = fco) = -8 R fくり) = fci-2) = 4.2398 > KMS %3D…

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Q: 6. y" + 3y'-2y e-2* [(4+20.x) cos 3x+ (26-32x) sin 3x]

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Q: S (x cos 2x dx) = Solve the integration 8 sin x + 11 cos x + c %3D II

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Q: 3(2 + cos t)3 +c Use the appropriate substitution to evaluate the following integrals: . sint (2+…

A: Solution is given as below:

Q: =²+2=+1 vi) Evaluate the complex integration (-1) (-2) -dz; C: |Z| = 6 7

A: Given integral is ∮Cz2+2z+1z-1z2z-2dz; z=6. To evaluate: complex integration of ∮Cz2+2z+1z-1z2z-2dz.

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: 2. f(x) = -5 cos (x) + 2 3. f(x)= 3 cos 2(x + 1) 4. f(x) = -sin 37 x - 1 PS = DCP= PS= DCP = PS =…

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Q: TL 2 Evaluate the integral: sin(3x)cos(3x)dx 3 1 A B C D H|m 3 16 1 3 16

A: To evaluate the integral. Option c is correct.

Q: 1 16r 10. Evaluate the definite integral | dr V16-r² 11. Evaluate the definite integral 4 + sin 2x)'…

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Q: f(x csc² 2x - x cos x cos 2x)dx

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Q: Q2 : Express the function r2 +r(sin0 + cos 0) = r² sin² 0 by %3D cartesian form

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Q: ull Pure Talk 12:55 PM 90% s3.us-east-1.amazonaws.com 1 | w(w2 + 1)³dw -1 x3 1 dx x2 sin30cos0 d0…

A: ∫-11ww2+13 dw=0, Since ww2+13 is odd.

Q: (x-2) (g-9) 2- 3X+uX- %3D 29-u | Sind general Salantion

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Q: sin (21 + 1) dt J cos² (21 + 1)

A: As per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: sin²x dx cos x

A: To decompose the given integral we have to use some basic trigonometric formulas.   We know that,…

Q: Cos z Residue of cos. at z = 0 is %3D 1. 1 -1 3. 2 4. 0 2.

A: The residue of a function: f(z) at z=a is defined as Resz=af(z)=limz→az-af(z).

Q: 1 Eliminabe the arbitrary constants C,e"cos 2x - 3X SIn 2x + - ZX Y C,e

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Q: Solve cos 8x dx. Determine a change of variable from x to u. Choose the correct answer below. 8 A.…

A: we put 8x=u so that dx=1/8du . see 2nd step.

Q: у" + 25у %3D 0, у(0) 3 6, у'(0) 3D —4 Y(x) = | 5 cos( 5x) – sin(5x) sin (5x) x

A: We have given differential equation y"+25y=0 with initial conditions y(0) =6, y'(0) =-4 We have to…

Q: cos(x) dx = dx. Use - 0o (1+x²)² o cos(x) 00 cos (x) Compute Jo 1+x²)² dx. Note that 2 (1+x2)2 the…

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Q: 13. S /(1– cos x)dx

A: Follow the procedure given below.

Q: integral cos^7(4x)

A: To find the integral

Q: CoS cos³ 0 5./ d0 1-sin0

A: Given problem:- ∫cos3(θ)/(1-sin(θ)) dθ

Q: сер 3 Substitute the expressions for u and v in the integral. x cos 9x dx = x sin(9)x sin( x) dx…

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Q: 5 sin r Question 3 (The Substitution Method for Definite Integrals). Calculate dr. (3+2 cos r)2

A: We use substitution method to solve above integration ..

Q: The coefficient of sin(x) in the antiderivative of F(x) =| cos 2 %3D

A: Given: F(x)=cosx26

Q: Sræsin(x³/2)dx= cos(x3/2) + C A 2 B) -을 cos(x3/2) +C ©-3/2 cos(x3/2 ++ C) C 2 D /xcos(x³/2) + C

A: Given: Let I=∫x sinx32 dx To Find: To evaluate the given integral.

Q: ** The definite integral " - 1/4 • 1/4 tan-1x² + /x²+ 1 Cosx +2 dx is equal to A 1 • T1/4…

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Q: O 1:0: d (sin-x?) = (sin-1; dx 1 d V1 - x² dr (x²) خيار 4 1 V1- x4 2x V1-x2

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Q: 5) Evaluate the real integral 27T 1 de (5+ 3 cos 0)(13+5 cos 0) by complex variable methods, i.e.,…

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Q: cos z Can you use p instead of p- 1+ z2 eiz to obtain the integral for cos x dx? o 1+x2 1 + z2

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Q: 2. Evaluate the integral : 6+x-5x dx x3

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Q: 2 sin x Verify whether the function g(x) =1- is the solution of the integral equation [1 – (7/2)]…

A: The integral equation gx-∫0πcosx+tgtdt=1 is a Fredholm integral equation. We have to check whether…

Q: QIN Evaulate : f v2 + cos4t sin4t dt

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Q: Cos 4x b. .J dx,u=1+2 sin4x (1+2 sin 4 x )*

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Q: SR(-1)" – 1)) x – 6n si 6T < x< 7n cos nx = { 8п — х si 7п <x< 8п n=1 +

A: The Fourier series of the function fx on -L,L is as follows. fx=a0+∑n=1∞ancosnπxL+bnsinnπxL. Use the…

Q: 3 2e + 4 sin x a.

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Q: J (sin 3x)² = sin 3x xp- sin 3x CO = sin 3x xp- sin 3x On simplifying further, y2 (x) = cq sin 3x /…

A: In this question , constant is to be included in the last solution of the differential equation.…

Q: 10. Prove that 7/2 75/2. sin 0 cos (cos a cosec 8) de 10 T 2 (1-cos a).

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Q: Test for exactness and find the general solution of: (cos2y – 3x²y²)dx + (cos2y – 2xsin2y – 2x³y)dy…

A: To solve the following differential equation

Q: Find a general solution. Show the details of your work [3] yi = y1 + Y2 + 10 cos t y2 = 3y1 – y2 –…

A: See the attachment

Q: -3 cos (2x)+sin(2x) in the form Rsin(2x+a)where R>0 and 0 <a<2n. Express

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: 9. Using integration by parts, Then k is? (a) - 1.5136 [*²x³ cos(x²) dx = k − [*³x sin(x²) dx -…

A: Given integral is ∫02x3cosx2dx

Q: y" – 2y' + y = [-6x – 8] cos(2.x) + [8x – 11]sin(() 2x) %3D

A: We have to solve the differential equation y''-2y'+y=[-6x-8]cos2x+[8x-11]sin2x.

Q: 4.5 Can you show me all the steps to solve this problem? Directions: Evaluate the definite integral.

A: Assume u=pi*t/2 From there find dt.When t=0, then u=0When t=1, then u=pi/2

Q: r = sin 0 + 2 cos² 0

A: Given

Q: ¹{.(²-1)} = Q4. C-1 (a) cosht - 1 (b) (c) 1 2 (d) 1 - cosh t [cos 2t - 1] [sin 2t - 1]

A: Here, to find the inverse Laplace transform of the function: 1s(s2-1)=1s(s-1)(s+1) Now, using…

Q: cos² x d.x 4 sin* x 2.

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Q: C. Evaluate the definite integrals ( show your solutions) 1. S, (x³ – 6x² + 2x)dx - TT 2. 3 cos3…

A: The given questions can be done as follow:

Q: Section 11.6: Calculus of Vector-Valued Functions - #49

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