Compute the following Cauchy principal value integral: dx р.v. x4 – 1 п/2 -T/2 Зп /2 -27

Q: 7x2 V2x3 - 1 dx .2.

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Q: Which of the following is a particular integral for the follo d'y 3d-4y te dt2

A: J

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

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

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Q: Evaluate the integral.

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Q: can i get step by step help please

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Q: If F = (x + y, x² - y) a= y = √, calculate fr F.Tds by using computing the line integral directly.)

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Q: Compute the value of the following improper integral. If it is divergent, type D. 1 dx 0.

A: To compute the value of improper integral.

Q: Calculate the iterated integral. 3 Vs+t ds dt

A: Consider the iterated integral

Q: If | h(t)dt = 24 %3D and 8 |h(t)dt = 10.6 what does the following integral equal? h(t)dt- %3D

A: We know, ∫abf(x) dx = ∫acf(x) dx + ∫cbf(x) dx         (if a<c<b)

Q: 1 Show J xd|x| = 1, by definition of RS-integral. %3D -1

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Q: cOsy du dy

A: Definition used-    Double integral -                             ∫ab∫cdg(y)f(x)dxdy…

Q: compute the value of the following improper integral. If it is divergent type D. dr (5x+1)

A: To compute the value of improper integral: I=∫1∞1(5x+1)2dx...(1)

Q: Compute line integral of F(x,y) = (2x² – 3,₁²³)^² + (2x +34²) ↑ с over the following C F-dr SCF ¾ ç…

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Q: Evaluate the integral. ∫t3  et dt

A: ∫t3  et dt  We need to evaluate the integral.

Q: r2 dt V4 + t?

A: The given integral is: I=∫02dt4+t2

Q: Evaluate the integrals in Exercises 1. esin (e) dx 2. e cos (3e – 2) dt

A: Given the integration I=∫exsin(ex)dx

Q: What is §3dx, §5du and §e^u dt? Those are integrals

A: a) We factor out 3, then integrate. c=integrating constant

Q: Evaluate |- e*dz where c is |z|=3 using Cauchy's integral formula „(1+2),

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Q: What is the integral of fcos (2t)dt? COS

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Q: 2. Evaluate the integral using FTC Part 2. d e²-t st². t dt dx

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Q: Calculate the iterated integral 2 So Só Væ + ydædy

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Q: Compute the value of the following improper integral. If it is divergent, type D. 1 dæ ¤ (In(x))

A: We have to check weather the given Integral is convergent or divergent.

Q: Evaluate the integral f(Vt,et) dt. t+1'

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Q: F(x) = sin(t) dt %3D 3x

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Q: Evaluate the integral. dt V 4 + t2

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Q: Evaluate the integral: ∫ t2 sec2(9t3 + 1) dt

A: The given integral is, ∫t2 sec29t3+1 dt. Apply the u-substitution by taking u=t3. Then dudt=3t2.…

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

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Q: Evaluate the integral.

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

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Q: Given

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Q: 2. Compute the following integrals: sin(it) dt; t - T 1 -dz; 1 22 (1,1) -

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Q: Calculate the following integral by applying the transform u=(3x-y)/3, v=y/3 and integrating over a…

A: Given,            ∫06∫y3y3+13x-y3dxdy                               (1) and                u=3x-y3…

Q: t * et  Compute the convolution integral.

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Q: Which of the following evaluates the double integral xy dA,

A: We can solve this as follows:

Q: In Vi - dt 3t (b)

A: ln(a)b= b ln(a)

Q: Use the local linear approximation of (1 – x)2º at xo O to estimate (0.99)2º. %3D

A: The linear approximation of f(x) at x0 is given by L(x) = f(x0) + f'(x0) (x-x0)

Q: compute J secx dr. I n trying to integrate

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Q: Evaluate the integral. 4 2t 9 -i- j+¬Vt k dt (9+?)*

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Q: Evaluate the integral S (* In ti+ 3t sin (t*) j+ k) dt. x(*+1)

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Q: Calculate the iterated integral. ds dt

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Q: Evaluate the integral.  integral  t  3sin 2  t dt

A: To evaluate the integral: ∫3sin2tdt. We know that, sin2x=1-cos2x2 Therefore, using this formula,…

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: Evaluate the integral: -2e 2е π/3 ₁² /³ tlnu tans ds du dt 0

A: In this triple integral we first integrate with respect to 's' then with respect to 'u' and in last…

Q: Evaluate the iterated double integral. I 3 3y be dady A

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Q: . Evaluate the integral S (t* In ti+ 3t sin (t*) j+ ) dt. +1)

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Q: 5, set up the appropriate iterated integrals in rios for I f dV on the indicated domains.

A: Step:-1 Given that  The equation of tetrahedron is z = 4 -2x -y⇒2x + y+z =4 ---(1) so, bounds or…

Q: Use the Substitution Formula in Theorem 7 to evaluate the integrals in Exercises 1-24. 2. а. rV x3…

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