Evaluate the definite integral. ra2/9 x° + a² dx (a > 0) 3 20 27

Q: Find the value of the following integral: cos2r dx,a>0 -1+a²° O 27 ат 2

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Q: Evaluate the definite integral. ra?/3 xVx6 + a2 dx (a > 0)

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Q: sin(x) cos (x) dx

A: Solution by substitution

Q: Find the integral of ([sin(x)]^6)([cos(x)]^7)dx from x=0 to x = pi/2. a. 14/1001 b. 15/2002 16/3003…

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Q: 3 3x - sin(Tx?)dx

A: Since you have asked multiple questions in a single request, we would be solving only the first…

Q: Find the value of the following integral: * COS2 dx,a>0

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Q: Evaluate the definite integral. + 3)(x2 + 3 x - 6)³ dx Need Heln? Read d 1t Watch It

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Q: Evaluate the definite integral. cos(T2) dz sin 8n Answer:

A: The given integral:∫08cosπxdxWe need to evaluate the above integral.

Q: Evaluate the integral: 1 A 6 B С 3 D HIM P 16 sin(3x)cos(3x) dx

A: Solve by integration

Q: The integral of the given function cos xdx is equal to а. 1 b. 2 С. -1 d. 3.1416 e. None of the…

A: We know that the integration of cosx is sinx then use the limit and calculate it. Option a is…

Q: Question 9. Work out the value of the definite integral (8x + 9)*dx 1 in the form: [BP – C"], where…

A: ∫12(8x+9)5dx

Q: Evaluate the definite integrals. 7/4 a) z tan(x?) dx b) [ 5a*e dx

A: (a) ∫0π/4xtanx2dx Let, u=x2 The derivative of the above equation. dx=du2x The lower limit is, a=02=0…

Q: Find the integral | e2 sin(3r) dæ +C

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Q: To evaluate x² /1-x² dx using trigonometric substitution, what is the new integral in terms of 0 ? A…

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Q: The integral of (10*/cos 10*)dx may be written as A In sec B* + tan B* | + C. Where A, B, and C are…

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Q: 71. Perform the following definite integral. 2 |(1-e-/2) dx = x=0

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Q: dx The integral can be transformed to which of the following when trigonometric substitution is…

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Q: The integral of the given function 7 cos xdx is equal to а. 1 b. 2 с. -1 d. 3.1416 e. None of the…

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Q: Evaluate the definite integral: T/6 sin8 cos e de

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Q: Q2: Solve the following integrals: (3) dx

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Q: Find the value of following the integral: ☎ COS²T -π1+a* S². dx,a>0

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Q: 3. Evaluate the integral sin ede from 0 to pi/2. A. 2x/3 B. 3π/5 C. 3m/16 D. R/4

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Q: Determine how large the number a has to be so that 1 dx

A: We have to find out the value of a .

Q: sin 4x Given: cos?(4x) (2 – 3 sec 4x) d× what is the appropriate formula to find the integral? ®…

A: Given that ∫sin4xcos24x2-3sec4xdxSolution :∫sin4xcos24x2-3sec4xdxlet,…

Q: cos e d0 Jo 1+sin? A 2

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Q: Refer to the definite integral to answer the following questions 3 1² (2²) (x²) dx

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Q: Evaluate the definite integral 2 (sin t, cos t) dt. COS 7/2 Select the correct anSwer helow:

A: We have to find out

Q: 1/3 13 sin t dt cos? t

A: Find the given integral

Q: 18. e cos 20 d0

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Q: Evaluate the integral. sin(0) d6 T/6

A: As we know that; The fundamental theorem of the integral: If Fx=∫fxdx then ∫abfxdx=Fb-Fa And…

Q: Q1/ Evaluate the following integrals: (a) / sin' cos를 dx. (b) S dx . (e) Sr² G- 1) dr .

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

Q: Evaluate the definite integral. 1/2 + a? dx (a > 0)

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Q: dx U x" Jx? +3 4

A: To find out the integration.

Q: Q: Solve the following integral Sx x sin-1 x dx

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Q: Evaluate the given integrals. 2. S sin?x sin 2x dx

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Q: Evaluate the following definite integral. cos(0) d0 1/2

A: The given definite integral is: I=∫π2π cos(θ) dθ

Q: To evaluate the integral x2 dx, Vx2 - 4x + 20 using trigonometric substitution, wh substitution…

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Q: * T14 Evaluate the definite integral: a sin? 4x cos² 2x dx T/16 O T/8 O T14 t/32

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Q: 3. The following definite integral equals: a. √2-2 b. 2-√2 c. 2+ √2 d. None of the above answers /2…

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Q: r? +3 dr 2

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Q: Evaluate the definite integral 05/dx. Give an exact, completely simplified 0.5_6x² answer. Hint:…

A: Use  substitution method for solving integral.

Q: sin t ( 10 + COs t)3 7 - sin 4x dx |

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Q: (d) Find the following indefinite integrals. xer (i) 1+e? xp. (ii) | cos (2r) sin (2r) dx

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Q: 2. The substitution u=cosx is suitable to solve the following integral: sin'x -dx cos 5x O False…

A: We have to check

Q: T/° cos® 3 0de Co.

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Q: x dx x² + √√x²-1-1 The integral - (A) cose de can be transformed to which of the following using…

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Q: ?T f(t)=√ t` cosnt dt ((나) ans = 4 12 The easiest way to solve the integral so that the result is as…

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Q: Given: dx Using trigonometric substitution, solve for the integral form in terms of 0. 0 d® B sin² 0…

A: Given: ∫x2-9x3dx Let I=∫x2-9x3dx   To solve this integral we need to do the trigonometric…

Q: (7) Evaluate the definite integral. | sin?t cos tdt

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Q: Q.35 The integral sin ede is given by

A: 35 Given integral is ∫0πsin3θdθ Since, sin3θ can be written as sin3θ=sin2θ⋅sin3θ Hence,…