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Q: Evaluate the integral. 1 dt t3 V2 -4

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Q: Find the formula for the function represented by the integral dt 6t+3 %3D

A: use the substitution method  for finding the integral

Q: Evaluate the integral ∫1/ √tcos (√t+3)dt

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Q: Verify if div(curl F) = o for = (x - y) i+ (x +y)j+zk.

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Q: Evaluate the integral J dx using the two-point Gaussian quadrature rule. 16+z*

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Q: Evaluate the integral. dt e dt = %3D

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Q: Let h(y) = In(y In y). Find h' (y). Show your work.

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Q: Find the normal line to f(x)=ax^2-3ax at x=2. Assume that a is a positive constant.

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Q: Verify that the integral of the beta density from −qto q equals 1 for(a) α = 2 and β = 4;(b) α = 3…

A: The Beta density function is given by: We need to prove:

Q: Evaluate the integral: ft² ns te" du ds dt

A: Let's evaluate given integral.

Q: Evaluate the improper intergal 1 dx using the residue (x2 + 9)* theorem.

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Q: PewHite F in sphethal cordmates and compute its diergence.

A: The divergence of F is 3

Q: i) Assume a MA(1)-process given by Y = c+ e +6ɛ,-1, E, ~ N(0, o?), t= 1,... ,T. Compute the…

A: A time series is a sequence of observations taken sequentially in time.

Q: Find the normal line to f(x) = ax - 3ax at x=2. Assume that a is a positive constant.

A: The given function fx=ax2-3ax at x=2.   Formula used:   Formula for finding normal to the function…

Q: Evaluate the integral | t(sec t2)4 dt

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Q: Find the local linear approximation of f(x) = In(5 + x) at xo = -4. %3D In(5 + x)

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Q: Find the center of mass of the thin plate bounded by the graphs of the given functions. g(x) =…

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Q: It G acts set tdansikivey then show that y Salgdnap Hof 0n A by to the actioh af en A fusthus then…

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Q: Evaluate the integral i- te*j + VTk] dt 0,

A: ∫03t2i - tet2j + t7/2k dt [t3i/3 - et2j/2 + 2t9/2k/9 ]03 9i - e9j/2 + 2*35/2k (9 , -e9/2 , 235 )

Q: + (xytl) Determine the Linearity of this DE. * ya dy y dy O Linear O Non-Linear

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Q: Derive the Simpson rule with f(x) = ax^2 + bx + c going through points xi−1, xi, and xi+1. Determine…

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Q: Find the integral. e3t dt Vest - 3 %3D 1

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Q: byparts VE tan! (VE) dt

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Q: Use the Fundamental Theorem of Calculus to find the area under curve of c)= 6z 4 13 between I=14 and…

A: Given function: f(x)=6x+13 Definition: Fundamental theorem of calculus: It states that f is…

Q: Find the solotion of the differential eaoation thot satisties the qiven nital condiion

A: The given differential equation is,

Q: Find the integration of S ecosx dx using Trapezoidal and Simpson's Rules

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Q: Evaluate the iterated integra x2y dx dy o Jo

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Q: Given

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Q: Evaluate the integral f 2x ¡dx using the two-point Gaussian quadrature rule. 16 \\frac{2}{3}\)

A: Given integral is ∫−222x216+x4dx. We have to evaluate the given integral using the two-point…

Q: Evaluate the integral. 2 | 7t sec -'t dt 2113 | 7t sec - 't dt = 2113 (Type an exact answer, using t…

A:

Q: Evaluate the triple integral: 2 x (Iny (z) dzdydx

A: ∫12∫1x∫y2ln(y)zdzdydx=∫12∫1xz22y2ln(y)dydx=12∫12∫1xlny2-y4dydx Now,…

Q: O Set up integrel for the Velume aboud x. 3 X= Y-2

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Q: Compute algebraically the resultant of the following complanar displacements: 100 N at 30°, 141.4 N…

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Q: Write down the definition of the laplace transform in terms of an improper integral and use it to…

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Q: Find the normal line to f(x) = ax - 3ax at x=2. Assume that a is a positive constant. %3D

A: Given: f(x)=ax2-3ax & x=2 To determine: Equation of normal line to given f(x)

Q: nsi Sinhna (na)? 8. ) Sind( x) Sin y)

A: Given Fourier series, ux,y=∑n=1∞1sinhnπ8sinnπ2nπ2sinnπ2sinhnπy2+8nπ2-8cosnπnπ2sinnπx2sinhnπy2 To…

Q: Find the Selution of (1-t +3t)4 (t) di - , (2) In which IL) denoter Bessel function

A: Leibniz integral rule : ddx∫bxaxFtdt=∫bxax∂∂xFtdt+Faxddxax-Fbxddxbx   Linear Volterra Equation of…

Q: Compute the path integral of F = ⟨ y , x ⟩ along the line segment starting at    ( 1 , 0 ) and…

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Q: Evaluate the integra 7/t dt 7/t dt = t2 %3D

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Q: Consider f dr. V1-16z² For the u-substitution u = 1 – 16x², which is the new integra 32 u2

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Q: Provide a homotopic squared parameterization of side one o_1= [-1,1] x [-1,1], other than this, and…

A:

Q: a Use parseval's identity to prove that dt TC (a² + )(b + ?) 2ab (a + b)

A:

Q: fx'e* dx ets

A: To evaluate:                     ∫x2 ex3 dx

Q: . Find a branch cut of log(z- 1) that is analytic at all points in the plane except those on the…

A: Branch cut of the complex function

Q: Evaluate the in tegral (x+ 2y) dy

A:

Q: Evaluate the integral. 4VE e dt Vt 4VE e dt =

A: This is case of integration by substitution where we look for an derivative in the integrand.

Q: B.) SET up THE DEPINITE INTEGRAL OF THE SHADED REGION THAT WILL GIVE THE PARAMET ER AND AREA

A: Note:- sin2θ =2 sinθ cosθ Area = ∫r2 dθ Given that  C1 :  r=-3 sin2θC2 :  r= 3 sinθ

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.