6. Evaluate the following real integrals by residue theorem 3 ーン ans : 493 • I= ST dX ans 8 12 (btX)(いちメ)

Q: 3 4 dx x2 + 9

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Q: 1. What should be A for the path independent of (2,4) ry + A 2Ay – 1 dy y? dr+ (1,2) Moreover…

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Q: Compute the Cauchy principal value of the following integral using residue theory details): 2+1 dz…

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Q: G.. Evaluate the fallowing real integrals by residue. theerem 3 -bm e 응) co3 mx (x4a?) Cx+b?)

A: This is complex analysis problem, we apply the residue theorem to solve the problem.

Q: Evaluate the double integral of cos(x) with x from 0 to π/4 and y from 4y to π

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Q: Use the Residue to Evaluate the following Improper integral: dx x² + 2x + 2

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Q: calculate the integral of  integral of 0 to 4 for dt/64t^2+9

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Q: Use the Residue to Evaluate the following Improper integral: dx x² – 2x + 2

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Q: Use a substitution of the form u = ax +b to evaluate the indefinite integral belov 7x+1 dx 7x+1 dx%=

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Q: Evaluate the integrals in ∫2y dy/y2 - 25

A: Given integral:

Q: Use a substitution of the form u = ax + b to evaluate thefollowing indefinite integrals.∫e3x + 1 dx

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Q: 2. Evaluate each of the following line integrals in two ways*. F (x, y) = (2x – cos y) i + (x sin y)…

A: 2. (a) Directly: The equation of the curve C1 is x-4+y5=1( intercept form), or, y=54x+5. The…

Q: 24 Use properties of integrals to evaluate S (2x – 1) dæ,if 3 11 24 S (2x – 1) dæ = 104, and f (2x –…

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Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: 4 3 1…

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Q: Evaluate the derinite Integral. #5 In(x) dx

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Q: Evaluate the definite integral (from 5 to 7)∫(d/dt (2+2t^4)^(1/2) dt using the Fundamental Theorem…

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Q: dx 2 -o x+4x+5

A: The general form of a complex number is given by , where a, b are two real numbers and . Any complex…

Q: Identify the type of generalized integral +00 fx'e* dx- and in continuity (if converging) to be…

A: According to question,Given Integral,Let I= ∫0+∞ x2ex3 dx

Q: Evaluate the integral: S/2 sin(4t - u) du dt

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Q: Use the method of u-substitution to evaluate the given integrals. 4t dt 2 – 812

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Q: 21. Write the definite integral that repre formed by y = x² + 2x + 1 and y=2x+5. Do:

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Q: 2/in Jin3 e dxdy a) By using the change of order evaluate the integral y/2

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Q: (4 b Prove that 5 foxx dx = K (6-a) using definition of integral, where fø= k [a,b], on

A: Given function is fx=k on a,b. We have to prove that ∫abfxdx=kb−a. Take Left hand side  Use Property…

Q: 2x(x+, こメP

A: Solve

Q: Consider the following propositions associated with the study of the +∞ dx J - 1.1² √6 +1 improper…

A: Given : ∫1+∞dxx  in which 1x6+1≥1x

Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z sinh z Where u> |z| > 0

A: Prove,∫z=1dzz2 sinh z=-πi3 ∫z=1dzz2 sinh z=∫z=1fz dz .........equation 1 fz=1z2 sinh z , 0<z<π…

Q: In evaluating /(3r2-1)2 dr by substitution where =3r2-1, what will be the resulting indefinite…

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Q: If 3 h(t)dt = 5 5 and .3 h(t)dt = 7.3 what does the following integral equal? h(t)dt =

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Q: Finel the integraL of finchio XSina) wher ne 5 and (0,2) by Simpsors rule 3.

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Q: 7. Use the Fundamental Theorem of Line Integrals to evaluate S(6xy, 3x² + 6y²) · dr where C is any…

A: Line integral theorem

Q: Consider the integral 2 6z² In(z) dz

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Q: 4t dt 2 - 812

A: To find the given integral integration (3 to 5) 4t/(2-8t²) dt

Q: 8r dr. 4. Evaluate the improper integral or show that it diverges:

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Q: 10. | Vi(1? + 31 + 2) dt

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Q: Evaluate the integrals. In 3 6tei + Te'j+ 2 ln tk dt 18(In(3)-1)i+7(3-e)j+2(In(3))(

A: Topic- integration

Q: In Vi - dt 3t (b)

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

Q: 2. Evaluate these indefinite integrals: dt (d) S; dt 2t2+5t+3

A: Given that a integration  and we solve it by using general property of integration. Here i attached…

Q: Jy cosy smy dy 3

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Q: 6. Compute the following integrals using Residue Theorem. 5z - 2 a. dz S dz b. So 22(2-1)" z(z-2)4…

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Q: Show detailed solution for the following integral: (Non-anonymous questionO) S tan'z sec³z dz 7

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Q: Evaluate the integrals

A: Given information: ∫141ti+15-tj+12tkdt

Q: Evaluate the integral. I sec (8x) dr tan(8z) In(cos)(3r) 64 +C X

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Q: - Prove using integrals Proper tos : e even sin()fc) dx=0 -b 9- For even functions.

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Q: 2. Calculate the indefinite integrals for the following functions as integr 1 (a) x In r/(In x)2-1…

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Q: Select the improper integrals in the following list of definite integrals. 2 7dt o 1-t2 1 9x In(x)dx…

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Q: Evaluate the improper integral dz, if it exist (x² + 49)2

A: Here we have to evaluate the given improper integral.

Q: Evaluate the integral dz dy dr. -2 Jo 5-722-7y2 32

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Q: Consider the integral 2x [2 dz. 4 Use the composite Simpson's rule with n=3 to approximate the…

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Q: 6. Compute the following integrals using Residue Theorem. 5z - 2 b. dz a. √21-23 = dz · Soz (²-2) 4…

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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…