Consider 7(t) = (2t³ – 2, 3e“, – 2 sin(3t)). Find Don't include the +C. %3D

Q: cos 2t dt 2.

A: Given:             ∫-π3π31-cos 2t2 dt Take the constant out: ∫a·fx dx=a·∫fx dx…

Q: 1 Show that L-1{ = (sin hat sin at) s4+4a4, 2a²

A: It is given that, L-1ss4+4a4=12a2sinhat sinat. A partial fraction decomposition of ss4+4a4:…

Q: 15. Find a) fxedx b) dx using the substitution of x- cos t.

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Q: 4sin 5x cos 3x-4cos 5x sin 3x/rom x= 0 to x= 2m

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Q: B\ Suppose that = 4 cos? t , x = v3 sin(2t) and 0 < t < n. S d²y *= - tan(2t) and = -sec (2t). 1 dt2…

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Q: Verify that y = 7 sin 2x + 9 cos 2x is a solution of y" + 4y = 0

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Q: (cos 2y – 3x²y²)dx + (cos 2y – 2x sin 2y – 2x³y)dy = 0 |

A: We will find out the required solution.

Q: 1. cosysin2xdx + (cos²y – cos²x)dy = 0; by treating x as the dependent variable

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Q: Find dy for the following func tion s -니 y=(1+ cos zt)

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Q: In right AXYZ with hypotenuse XZ if cos X = and XZ 10 24. then to %3D the nearest integer XY = ?

A: Given: ∆xyz is the right angle triangle with hypotenuse xz x=710 &amp; xz=24

Q: x2 Vcos(t) +3 at 1. COS 2.

A: Given that, the integral ∫2x2cos t + 3 dt

Q: If the RHS (Right Hand Side-the source) function of a second-order differen tial equation with a…

A: Here we have to go option wise and choose the option with; y(0) = y'(0) = 0. Clearly we can see…

Q: 8F OF OF 1. Use the formulas above to find and ду ax exy + sin (xyz) + In (yz) = 4 – z

A: Partially differentiate the function with respect to x.…

Q: 5 Evaluate the integral 2x cos(xy)dydx 4 0.

A:

Q: Answer the following True or False: d Since dx d -sin (6x² + 3x + 4) = (12x + 3) cos x dx (6x² + 3x…

A: The objective of the question is checking the proper use of chain rule .

Q: Show that L{cos at} = S s² + a² Hence find L{sin 8t sin 6t}.

A:

Q: 3 O f sin 2x cos 2xdx 4)

A: we use substitution method

Q: Find the least order for homogen D. E. with constant coefficient which has the solution : 6.x3 +…

A: The nature of roots is given as:Corresponding part of C.F.Nature of roots of auxiliary equation1One…

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

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Q: (sec(In x) y ху" + у' +:

A:

Q: To evaluate 3cosx -1 1- sin?x dx, the integrand can be transformed to A J(3 cos x - sec²x) dx ® S(3…

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Q: determine the annihilator of the givenfunction. F(x) = sin x cos3 x.

A: We have to determine the annihilator of the function: Fx=sinxcos3x Annihilator is the set of linear…

Q: 2. Use Method of Undetermined Coefficients: y" - 2y' + 5y = 4e*cos2x + n IN

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Q: Evaluate the integral. 7/2 cos 6x dx COS -T/2

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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: dy Find if y = 5x² sin4x dr' O None -20x? cos4x – 10xsin4x 20x? cos4x + 10xsin4x O 10x? cos4x +…

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Q: Evaluate the integral 3 2x cos(xy)dydx 2

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Q: The solution of the DE (1+ tan x)y'=-secx coty is O None of these siny + In cosx| = c %3D sinx +…

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Q: xdx 2. V3x +5 sin 4x 4. 9+8cos 2x

A: We have to solve these integrations.

Q: 1.) Evaluate In 2 e*2arctan e* J (1+ e2x) sec(2arctan e*)' А.) -dx. ežr(1 – e*r)- (arcsin e 2x) cos²…

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

Q: Show that where n is a positive integer.

A: To show

Q: If we have to check the DE (x+2)* 5-8y-4xy for Exact then My = dx None of These 20x+2) -8 - 4x

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Q: Find the general solution to the DE using the method of Undetermined Coefficients: y" + 9y = 2…

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Q: Verify that y = 7 sin 2x + 9 cos 2x is a solution of y" + 4y = 0 %3D

A: Given, y = 7sin2x +9cos2x  We have to verify y = 7sin2x +9cos2x is a solution of y"+4y = 0

Q: 13 20 Find for Two only of the following: dx 1- y=xtanhx 2- y =cosh 3x- sinh²3x

A: We have to find derivative

Q: Q1\ Differentiate the following (c 1)2xsin-13x 2)y = In *+1 Vx-2 %3D 3)y %3D sin-1 2x

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Q: evaluate the Cauchy principal value of the given improper integral. cos 2r dx x² + 1

A: We have to find the Cauchy principal value of the improper integral. First we have to write the…

Q: If y = (x – a)/2ax – x² + a² sin¬'(÷ prove that y' = 2/2ax – x² a is constant.

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Q: Evaluate: Jx°cos(2x)dx A None of the given choices 2x2sin(2x) +2xcos(2x) + sin(2x) + C 4…

A: I have used the by parts rule of integration and get the required integral . Option (D) is correct.

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

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

Q: d²s dt2 sin 3t + cos 3t |

A: In this question, we need to find s.

Q: 1 Evaluate the equation /o x² sin (xy)dydx

A:

Q: Evaluate: Jx?cos(2x)dx A None of the above 2x2sin(2x) – 2xcos(2x) + sin(2x) B + C 2x²sin(2x) +…

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

A:

Q: Find the general solution of the DE: dy/dx = sin(7x) cos(5x) + cos(7x) sin(5x).

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

A: this is false because

Q: Find the general solution of the following first-order ODE xy' = y + 2x' sin² (2)

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Q: Suppose f (x) =cos( 2– 3x). Evaluate: )dx A - 3sin(3x – 2) +C ® -;sin(3x – 2) + C sin(3x – 2) + C D…

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