1 Evaluate the improper intergal dx (x² + 16)² using the residue theorem. 8.

Q: 8. Find the general indefinite integral (x³ -2² + x)dr; b) / (2" +-)dr, x > 0; c) (sin(3t) +…

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Q: 5. Use Green's theorem to evaluate where C is shown below (6y - 9x) dy — (xy - x³)dx (-1,4) (-1,-1)…

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Q: 3. Evaluate the indefinite integral e* –3 -dx (e²x +1)(e* – 2)

A: Consider the equation

Q: 2. Use the Definition of Residue to show that: dz -ni 3 Jizl=1z² sinh z Where 0 < |z| < T.

A: Image is attached with detailed solution.

Q: 4- 2x Evaluate the following integral : dx 2x +4,

A: The answer is π/3.

Q: dx. Evaluate the integral / (x² + 1)(^ · x – 2) -

A:

Q: 3. Find the indefinite integrals. (a) /4 dx (b) /2* r 2x-x2 dx

A: Given two functions integrate it by use of formulae

Q: 9. Evaluate the integral J 4x2+9 1 dx

A: We can solve the integral as below.

Q: 5. Write a 5th degree Taylor polynomial for f(x) = cos(2x) centered at x = T/4. %3D

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Q: Q6) Compute the integral 3 1 dxp -з (х +2)3

A: Here we solve the given integral.

Q: 13. Consider the integral | - dx then (which statement(s) is/are correct): x2 - 4x (i) dx : x - 4x…

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Q: Find the indefinite integral. 1. 16 + t² dt * (x² + 4)³/2 + 4)3/2 2. -dx-

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: Evaluate the integral.

A: Given integral: ∫121241-x2dx

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: Evaluate the integral. 9 17 1+ x2 dx V1- x2 +C

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Q: 4х+2 Evaluate the integral -dx. (Hint: Use Algebra to help further rewrite your (x² +1)(x=1)…

A: First break by using partial fraction then integrate

Q: 9 Evaluate the integral f 2x (x² + 1)° dx using the substitution = x² + 1. и — с 2.x (x? + 1)° dx +C

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Q: 1. Evaluate using the Fundamental Theorem of Calculus: 1 1 dx x2 (a) - -2

A: Given: Let I=∫-2-1 x-1x2 dx To Find: To evaluate the given integral by using the Fundamental Theorem…

Q: Q5) Evaluate the integral 0.61-10 (6.73x + 4.3025 - 10- dx 2.316 • 10-11 122-10- Using trapezoidal…

A: The solution to the integral can be calculated using numerical methods. The formula for the…

Q: Evaluate the integral. 7 √49-x² √49-x²-22 49-x² 1 √²-3³ (x² + y² + 2²)1/2 dy dz dx =

A: Solution:-

Q: 9-x2 18-x²-y² xydzdydx. B: Find the integral fo J

A: Triple integral

Q: Evaluate the integral. 7 7 √49-x² ILL 1 /49-x² (x² + y²)1/2 dy dx dz =

A:

Q: 4. Use the Fundamental Theorem to evaluate (x³ - 6x)dx . (Your answer must include the…

A: Use the integral of polynomial.

Q: 1 Evaluate the improper intergal | dx (x2 + 9)° using the residue theorem.

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Q: Evaluate the integral. x² - 81 | V=² x x² - 81 | Vx² x √x². 81 X √x². 81 X x² - 81 X 1² 1² - dx = -…

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Q: 7. Use integration by parts to prove that for any positive integer n, | cos"x dx = 1 cosn-1xx+ n - 1…

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Q: 4. Use residues to evaluate the improper integral 1t r4 a + x2 dx; where a is a real constant.

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Q: Compute dx using the techniques as presented in class and in our textbook. Show all 2x +5x-3 the…

A: we first factor the denominator

Q: (5x° + 4x + Ix Consider the indefinite integral dx x2 – 1 Then the integrand decomposes into the…

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Q: O f(3x² + sec² 2x) dx

A: Given query is to find integral.

Q: 10. Using the substitution u 2x - 1, prove that %3D 3 8 dx J1 (2x-1) 25

A:

Q: 1. Find an antiderivative of f(x) = 16–x². Then, use The Fundamental Theorem of Calculus %3D 4 to…

A: Given : fx = 16-x2

Q: 6. Evaluate the fallowing real integrals by residue. theerem 3 -bm -am 응) Co3 mX ans : X Sin mx ans…

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Q: 6.3.18. Evaluate the integral. using U substitution integrate (cos^2(x)sin^2(x))dx

A: Hello, there are two functions present in the question. As the first function comes along with the…

Q: 9-x2 B: Find the integral S 18-x2-y xydzdydx.

A: We have to calculate the given intregration

Q: 39. (a) Show that 1 1 > 0 2x V1+x² for x > 1. (b) Use your result in (a) to show that 1 dx 1+x is…

A: The compleet solutions are geven below

Q: 1. Evaluate the indefinite integral. Hint: U-substitution. 3 dx x In x

A: ∫ 3x lnx dx 3∫ 1lnx·1x dx

Q: Evaluate the integral. 고-36 x² – 36 . 6cos- (승) +0 /x² – 36 - dx = Vx² – 36 – 6cos¬! + C x² – 36…

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Q: 3.2 Let f(x) = Approximate the integral x4 x L f(x) dx using the Trapezoidal rule with n = 4. -2

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Q: 9. Evaluate the indefinite integral x'V4-x² dx . 3 Hint: Let u = 4 – x² and write x' = xx?.

A: Given ∫x34-x2dx

Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z2 sinh z Where 0 < |z| < T.

A: Use the following formulae, to evaluate the given complex integral. Let z0 be a pole of order n,…

Q: 7. | (x² + + 2x) cos x dx

A: Apply the integration by parts in the given integral. Let  u=(x2+2x) ; dv=cosxdxThen,du=2x+2dx ;…

Q: xcosr (i) Find the Cauchy principal value of the integral dr. ² + 4x + 8

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: Evaluate the integral. B 4х- 3 dx J2

A: To evaluate:

Q: -1 х2 Using substitution method, evaluate the integral Jo dx 0 x3+1

A:

Q: dx Evaluate the integral: 3/2 64 -

A: To solve the given integral problem.

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

A: Cauchy residue theorem is one of the method to evaluate the integral of analytic functions.…

Q: dx Evaluate the improper integral (x-3)2

A: Given query is to find the value of the integral

Q: Step by step

A: To evaluate the below indefinite integral