Evaluate the integrals in Exercises 1-22. 1. fon 3 sin dx cos 2x dx 2. x sin x dx sin“ 2x cos 2x dx 3. 4. Jow'rd sin³ x dx cos³ 4x dx 5. 6. 7. fan? sin x dx sins 8. dx 9/- 3 cos 3x dx os³ x dx 9. 10.

Q: Evaluate the integral: integral fom 0 to pi/2 sin^2 x cos^2 xdx

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Q: In the integral of x cos 2x dx with limits form 0 to pi/2, what is the indefinite integral? Select…

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Q: Describe strategies for solving the types of integrals given in Exercises 8–18. | cos* x dx, k odd |…

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Q: Evaluate the integrals in Exercises 25–30 by using a substitution prior to integration by parts.…

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Q: In Exercises 1–8, decide whether the integral is improper. Explain your reasoning. dx dx 1. 5х — 3 -…

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Q: Evaluate the integrals in Exercises 37–44. 37. Jau. cos x sin x dx sin³ x cos“ x dx 38. tan“ x sec?…

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Q: Only one of these calculations is correct to evaluate the definite integral /sinx dx Using the…

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Q: 14. Verify that f cotx dx = In(sin x) +C. (Do not try to solve the integral from scratch.) %3D

A: Given: verify that ∫cotxdx=lnsinx+c For verifying given integral, we integrate given integral

Q: Use reduction formulas to evaluate the integrals in Exercises 41–50. Ssin' 2 de 8 cos“ 2nt dt 42.…

A: Dear student, Since you have asked multiple questions in a single request, we will be answering…

Q: 3. Solve the integral by two grid in the y-direction and four grid in the x-direction with…

A: Solve the integral by two grids in the y axis and four grids in the x axis with Trapezoidal rule:…

Q: Evaluate the integrals in Exercises 45–76. 2(cos x)-1/2 sin x dx (tan x)-3/2 sec²x dx 45. 46. (20 +…

A: Hello thank you for the question. As per our guidelines we are allowed to answer one question. So,…

Q: Evaluate the integrals in Exercises 9– 18 It may be necessary to use a substitution first. x dx 9.…

A: We'll answer the first question since the exact wasn't specified. Please submit a new question…

Q: In Exercises 1-10, indicate a good method for evaluating the integral (butdo not evaluate). Your…

A: Let the integral be y - y = ∫xsec2x dx                             .......................(1)Using…

Q: Evaluate the integral: f sin 7x cos 2x dx. A) sin 5x + sin 9x + c. 2 B) cos 5x +co cos 9x + c. 10 C)…

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Q: In Exercises 15–22, graph the integrands and use known area formu- las to evaluate the integrals.…

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Q: Evaluate the integral. Sex. cos 3x dx e2x [ sin 3x + cos 3x] + C O e2x [3 sin 3x + 2 cos 3x] + C 13…

A: Given: ∫e2xcos3x dxe

Q: Find the indefinite integral using integration by parts with the given choices of u and dv. |x…

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Q: Evaluate the integral. 5n /2 2, 1 - cos t dt 3π/2

A: ∫3π25π21-cos2tdt=∫3π25π2sin2tdt=∫3π25π2sintdt=∫3π22π-sintdt+∫2π5π2sintdt=1+1=2

Q: Evaluate the integral by using a substitution prior to integration by parts. Sin(2x+2x²) dx Hide…

A: Given ∫ln2x+2x2dx

Q: |In Exercises 67–70, use the following alternative method for evaluating the integral J = f sin" x…

A: Consider the given formulas:

Q: Calculate the integral: /3 arctan(x) dr a) O 3x arctan x – In(1 + x²) + C b) O3 In | arccos x| + C…

A: we will apply the integration by parts rule: ∫(u·v) dx=u∫v dx−∫u'∫v dxdx And we also use…

Q: Evaluate the integrals in Exercises :: 1. / sinh 2x dx sinh đx 41. 42.

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: In Exercises 45 and 46, both substitution and integration by parts are used to determine the…

A: 45. ∫exdx46. ∫11+xdx

Q: Evaluate the integral. 3x cos 2x dx O e3x [2 sin 2x - 3 cos 2x] + C 13 O 1 [2 e3x sin 2x + 3 cos 2x]…

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Q: (d) Prove that 1-cos 2x dx is divergent. Hint: Split the expression inside the integral into two…

A: Integral is converges or divergence

Q: Use the tabular method to evaluate the integral |(* + 2x – 1) cos(4x)dx

A: Given:∫(x3+2x-1)cos(4x)dx

Q: In Exercises 27–40, use a substitution to change the integral into one you can find in the table.…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: Evaluate the integral. 3y- cos xy dy dx x/3 O 5(1 - cos 3) O 3(1 - cos 3) O cos 3 -1 (1 cos 3)

A: Given: ∫03∫x313y2 cos xy dy dx We have x3≤y≤1 and 0≤x≤3 This can be seen as: We can change the…

Q: Evaluate the integral f 2x ¡dx using the two-point Gaussian quadrature rule. 16 \\frac{2}{3}\)

A: Given integral is ∫−222x216+x4dx. We have to evaluate the given integral using the two-point…

Q: Evaluate the integrals in Exercises 1–12. 1. /e'sin e') 'cos (3e' – 2) dt e*sin (e*) dx 2. -1/4 TT…

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

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

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Q: Which integral computes arc length of f(x) = x5/2 on [0, 1]? 1 49 -x' dx 1+ 4 - 1 | V1+ x° dx 1 1+…

A: We have to find the arc length

Q: 3-Evaluate the integrals in Exercises: 2√3 So dx √4 + 4 + x² 0 4- 6 dx 5. Sot v Jo V1 + 9x² cos x dx…

A: We have to evaluate the integrals.

Q: Evaluate the improper intergal dx using the residue 2 (x² + 4)² theorem.

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Q: Step by step

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Q: dt cos°(2 sin" 21)/1– 4r cos(2 sin2t

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Q: evaluate the Cauchy principal value of the given improper integral. cos 2r dx x² + 1

A: We have to find the Cauchy principal value of the improper integral. First we have to write the…

Q: Evaluate the integrals in Exercises 1–6. (sin¬l x)² dx 1. dx 2. x(x + 1)(x + 2)· . · (x + m) 1 /sin'…

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Q: Evaluate the integrals in Exercises 1–8 using integration by parts. In x dx In (x + 1) dx 1. 2. |dx…

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Q: /2 etan y sec y х cos" ydxdy

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Q: Evaluate the following Integrals: 1. (sin(4t) – 3 sin(2t)“ dt 6. Vsech(4x) tan (4x) dx 3 sin sinh 3y…

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Q: You found that the reduction formula of a certain integral is In = 180 (13x" sin (13x) + næ"-1 cos…

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Q: 9. In evaluating the improper integral dx , which of the following is true? (1-3x)2

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Q: Evaluate the following integral. cos x dx -6x 1 sin 2x dx 2 - 6n O C. dx + cos 2x dx OD. dx + - 6x 6…

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Q: Evaluate Poisson Integral: In(1-2a cos(x) + a²) dx ,a.) [a| 1,

A: To evaluate Poisson's integral: ∫0πln1-2αcos(x)+α2dx  a)α<1 b)α>1

Q: Use the calculus of residues to evaluate the improper integral COSX -dx. (x²+1)³

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Q: Use the Substitution Formula in Theorem 7 to evaluate the integrals in Exercises 1-24. 2. а. rV x3…

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Q: Let u = cos(4x) and du = e² da, then by using IBP, the integral [e²= cos(4x) e2x cos(4x) dx is equal…

A: Given, u=cos4x and dv=e2xdx. Formula for IBP: ∫udv=uv-∫vdu