4.3 Use the calculus of residues to evaluate the following integral 27 1 1+8 cos? 0

Q: 3. (a) Evaluate the indefinite integral / 2/arctan(3r dr. 1+922

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Q: Evaluate the following integral. ∫ (6 + 3z)cos(1 + 4z)dz

A: Integration:        ∫(6+3z)cos(1+4z)dz=∫6cos(1+4z)dz+3∫zcos(1+4z)dzBy parts formula:∫uv…

Q: 1. Evaluate the following integral: +3) cos(5t) dt CAGIPIE your Where a=1 b=8

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Q: Q14: Compute the following indefinite integral х2+5х+6

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Q: Evaluate the following definite integral. 10 6 dy y² - 7y- 60 10 6 dy = [ y2 - 7y- 60 (Type an exact…

A: To find: The definite integral of ∫010 6y2-7y-60dy. Formula used: Integration formula:…

Q: 1 To evaluate the integral J dx, we substitute x = 3 tan 0-4. (z²+8z+25)*/2 Select one: O a. True O…

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Q: Csin $ 3 y cos*3 ychy

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Q: Evaluate the integrals

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Q: Compute the given indefinite integral. fir (2 – 4)(x + 3)dæ | +C

A: Given integral, ∫x-4x+3dx

Q: 7.1: Evaluate the following integral and show your work: S (2? + 1) e-" dæ, 0 < x < 1 е

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Q: 15. Evaluate the following definite integral. 1 | (4i + 3tj + 7t°k) dt

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

Q: 7) Set up the integral to find the area of one petal of r = cos 50 for - <0< 10

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Q: If we let u = cos t, then the integral [(sint). In (cost) dt can be expressed as - [In(u) du 0…

A: An integral is given. We have to write the substitution form of the integration in terms of the…

Q: Evaluate the following indefinite integral. 7 1+8t -dt 5t (Type an exact answer.) √ 1+8t 5t -dt=

A: The given integral is ∫1+8t75t dt

Q: 5. Find the indefinite integral. 38x xp, 1 a. In 3 na 38* +C b. 38x +C 8 In 3 c. 8(In3)3* +C d. 8x…

A: ∫38x dx Put, 8x=t⇒81=dtdx⇒8 dx=dt⇒dx=dt8

Q: 4. Use residue theory to calculate the following integrals: 3x (a) P.V. · Loo (2²+49) (2² - 2x + 5)²…

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Q: 17. Use the theory of residue to evaluate the following definite integrals r2 (a) /" (b) / do 2+ cos…

A: 17(b) ∫02πcos2θ dθ5-4cosθ=real part of ∫02πei3θ dθ5-4cosθcosθ=real part of eiθsinθ=imaginary part of…

Q: Evaluate the following definite integral ,-(s-2)t sin(3t) dt. 3 2 (8 – 2)2 + 9 (8 – 3)2 + 4 - - O 1.…

A: Properties of Laplace transform  Lf(t)=∫0∞e-stf(t)dt Leatsinbt=b(s-a)2+b2 Lsinat=as2+a2

Q: 1. Find the following indefinite integrals: 1 du b. fcos uchu = а. 1 fa'du- d. . du - с. 1+u? f. f-…

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Q: 8. Evaluate the integral: S 2r cos r dr

A: Given, ∫2r cos r dr We know that, ∫a fxdx=a∫ fxdx⇒2∫r cosr dr Now by using the Integration By Parts,…

Q: Make the given substitution to evaluate the indefinite integral. 28r dr .u= 3-r 3-r'

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Q: Use the calculus of residues to evaluate the following integral 1+8 cos² 6° de. d8.

A: Let I is the value of given Integral.

Q: 6. Evaluate the following real integrals by residue theerem 3 ans : 493 • I= dX ans 8 12 (bちX)(いゃ) ト

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Q: Evaluate the following integral. |5 cos (5x)dx 5 cos (5) dx |(Use C as the arbitrary constant)

A: The integral is given by

Q: Evaluate the definite integral. 1/6 Csc( 3πt) cot(3πt) dt /1/18

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Q: Evaluate the integral. 7/2 sin 8t sin 7t dt 16 O 31 O T5 3

A: the given integral is ∫0π2sin8t sin7t dt use the formula Sin C sin D= -cosC+D+cosC-D2 here C=8t and…

Q: Evaluate the integral sin^4 e de from 0 to Tt/2 * T/4 O 2r/3 O 31/16 О З1/5

A: We have to evaluate the integral ∫0π2sin4θdθ. Use the reduction integral formula, which is given…

Q: Evaluate the indefinite integral. | cos(8z) /4 – sin(8z) da = +C.

A: Let I is the value of given Integral

Q: Which of the following is one of the correct steps to evaluate cos3 dt to obtain the correct indef…

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Q: 24) Determine the following indefinite integral. |(3u-2 – 4u? + 1) du

A: To evaluate the integration.

Q: 9. Evaluate the following integrals а. se cx b. CO s x + co s(8z) – iz 3 -4x с. dr x? +1 -

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Q: Evaluate the iterated integral. /2 6 cos(0) Jo

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Q: (4) Evaluate the iterated integral ". Scos" 3r² sin 0 dr d0.

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Q: (8) 20. Evaluate the following definite integrals: (a) (5 sin z + 7 cos(2r) + 3 sec² r) dr (b)

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Q: Sn/2 "/2 cot3 x dx

A: Given: ∫π4π2cot3xdx

Q: Consider the following. 6. 13 In(x) dx Let u = In(x). Find du. %3D du = dx Indicate how the limits…

A: Let us consider the integral, ∫1913 lnxxdx

Q: Use the calculus of residues to evaluate the following integral: cos20 -de. 2 + cose

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Q: 1. Use substitution to express each of the following integrals as a multiple of Sadu for some a and…

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Q: 12. Consider the following integral Ssin2tcos2tdt and the statements (decide upon the correctness of…

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Q: 2. 36 +x² dx =)

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

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Q: Use the calculus of residues to evaluate the following integral: cos20 de. 02+cose

A: Given the given integral is ∫0πcos2θ2+cosθdθ

Q: 5. Evaluate the following integrals3 sin ttZ dz C: İz-il 471 =D2 ans: C. 3. coshz -27 ans : Icz²3iz

A: By residue theorem, we can solve these problems.

Q: 1. Evaluate each of the following integrals. Show all work. 7/5 (a) 2 cos(5æ) dr (b) 3 dt 4+ 5t

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Q: (6+ 3z) cos(1 + 4z) dz

A: We will use integration by parts

Q: (8) 19. Evaluate the following indefinite integrals: fcom"(32) sin(32) dz (b) (In r)7 dr

A: Explanation of the answer is as follows

Q: 3 In z/4 tan (2)+cos(r) gives a positive number. 3 3. The integral f dæ, when evaluated, O True…

A: Check if the given statement is true or false.

Q: Evaluate the definite integral. 1/6 csc(3nt) cot(3nt) dt /1/18

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Q: 5. Evaluate the following integrals 3 sin #Z dz, c 1z-il=2 24 -4 ans: 3 co shz

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Q: 2. Find the following integral: NT u sin du. n.

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