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

Q: 2. Evaluate the following integrals I de 8 (sin 20)

A: We have to find the value of given integral

Q: 1. Evaluate the integral: 2³ cos (dt du

A: Given

Q: Evaluate the integral. /2 15 cos Jo s x dx

A: Given:          ∫0π215cos5x dx        =15∫0π2cos5x dx         =15∫0π2cos2x2cosx dx…

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

A:

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

A:

Q: Use the appropriate substitution to evaluate the following integrals: (2 1 A 3(2+ cos t)3 + C -1 + C…

A:

Q: In the given question as follows, use Wallis’s Formulas to evaluate the integral:- See the question…

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Q: 3. Evaluate the following integral: S,72 35 cos (x) sin (x) dx

A:

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

A: Given integral, ∫x-4x+3dx

Q: 4. Use properties of integrals to verify the following inequality: 4. /4 sin xdx s 24 24 VI

A:

Q: 1 6. Evaluate the given integral using suitable substituion COs(V도+ 3) dr

A:

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

A:

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

A:

Q: Using the Simpson-1/3 rule (single version), give an approximation of the following integral 3.2 |…

A:

Q: 5. Evaluate the following integral: S/3x tan?(x) dx (Hint: Use a substitution first)

A:

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: 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: 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: 6. Evaluate the following real integrals by residue theorem 3 ーン ans : 493 • I= ST dX ans 8 12…

A:

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: (2) Compute the following integrals. /4 (a) sin (4r) cos (4.r) dæ. (b) cos(ka)e-lz dx, Hint:…

A:

Q: Evaluate the following integral. 2 6 cz/6 A dr dz d0 0. 2n c6 cz/6 A dr dz de = (Type an exact…

A:

Q: 5. Evaluate the integral: Jsin?x cos'x dx

A:

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

A:

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

A:

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: See images below

A:

Q: 1. Find the following indefinite integrals: a. G b. fcosudu = 1 c fa'du=- d. Jitu du = e. fsecu…

A:

Q: Evaluate the following iterated integral. 4 2 x cos y dy dx

A:

Q: 3. (a) Evaluate the following integrals: (1) / VE VzVE+1dæ sin 40 (i) / i do cos? 20 1+ (b) Find…

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

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Q: 9. Find the area of the region in the first quadrant that is inside r = 4 sin 0 and outside r2 = 8…

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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: 14.) cos" 0 sin" o do COS

A:

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

A:

Q: 14. 7/4 3x fe³ sin 4xdx

A: On solving this we will get

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

A:

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

A:

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

A: We will use integration by parts

Q: 2. Evaluate the definite integral. 4 *7 – 7sin²e do 3cos?e

A: I=∫0π47-7sin2θ3 cos2θ dθ1-sin2θ= cos2θI=73∫0π4 1-sin2θcos2θdθI=73 ∫0π41 dθ

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: Q2) - Evaluate the following integral: 1 1.25+ cos w

A:

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

A:

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

A: