answer (b) ONLY 4. Use residue theory to calculate the following integrals:3x(a) P.V. · Loo (2²+49) (2² - 2x + 5)²dr(b) fosin 3x(x2. +16)²dx

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Answered: 4. Use residue theory to calculate the…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 5E: 5. Prove that the equation has no solution in an ordered integral domain.

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5. Prove that the equation has no solution in an ordered integral domain.
(b) Let 2x 5x+9 ( - 1)(2+ 1). Evaluate the indefinite integral (z)dr. S(2)da. Hint: Do long division first. (c) Use (b) evaluate 2. +9e de.
I [20 / (e(8-10x) dx. The integrand equals 20 divided by [e raised to power of (8 - 10x)]. O 2e(8-10x) + c O 2e(10x-8) + C O 8e(10x+8) + C O 8e(10x-8) + C
Evaluate the following definite and indefinite integrals. V6 (a) da V3+1 (b) / da V3 – r2 (c) x* +x + 18 dr Your final answer can be a decimal rounded to 2 decimal places. r(3+ x2) (6x + 2x*) sec (3+ x²) dx Hint: Do some factoring first.
IV. Exercises A. Solve the following integrals: (1) / 20. (4) / 3* (5) /de (6) 32 5z+2 dr (2) / (2e + 4"). (3) 2(5") dar -1 dr 3x-1
d Calculate the integral 2r -x
Evaluate the following integrals using residue theorem: (a) Loo (x² +9)(x² + 4)²
4. Evaluate the integral below by following a series of steps: 2x +3 J 4x² + 5x + 6 (a) Evaluate f dx by using trigonometric substitution. 4x2+5x+6 Hint: Pull a 4 out of the integral, then use "completing the square" in order to write the denominator as (x + A)2 - B 2. Then use a trigonometric substitution. 8x+5 (b) Evaluate f dx (Don't think too hard! The answer is easy!) 4x2+5x+6 (c) Find constants C and D which allow you to write the original in the following way: 8x +5 dx + D| 2x + 3 dx 4x2 + 5x + 6 dx = C J 4x2 +5x + 6 4x2 + 5x + 6 (d) Use parts (a), (b), and (c) to evaluate the integral!
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4. Use residue theory to calculate the following integrals: 3x (a) P.V. · Loo (2²+49) (2² - 2x + 5)² dr (b) fo sin 3x (x2. +16)² dx