Evaluate the integrals in Exercises: -1/3 6 dx VI + 9x? 5- TT cos x dx Jo vī + sin²x Vi + sin²x 6- dx xVI + (In x)² 7-

Q: Evaluate the integral using the given substitution. Jx cos (6x?) dx, u=6x? x2 O A. sin (6x?) +C 2 1…

A: As per our guidelines we need to solve only one question.please repost the remaining questions as…

Q: Consider the definite integral. (8x – 1) e- dx Let u = 4x – x. Use the substitution method to…

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Q: Transform the integral fo o sin o sin 0 do de by the substitution x = sin o cos 0, y = sin ø sin 0…

A: Solution: The given integral is I=∫0π2∫0π2sinϕsinθdϕdθ The substitution is x=sinϕcosθ, and…

Q: Evaluate the integrals in Exercises  by making a substitution(possibly trigonometric) and then…

A: since you have posted multiple questions so I'll solve first one for you , for rest question's…

Q: Make a substitution to express the integrand as arational function and then evaluate the integral.…

A: Given integral is: Using substitution and applying derivative:

Q: use the indicated substitution to evaluate the integral.

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Q: tan (In |4x2|) -dx is b in cos (In |(2x)*|)|+c. The integral of What is b?

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Q: To evaluate f x?Vi – x²dx using trigonometric substitution, what is the new integral in terms of 0?…

A: We are given with the integral and evaluated

Q: Use a substitution of the form u = ax +b to evaluate the indefinite integral belov 7x+1 dx 7x+1 dx%=

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Q: Evaluate the iterated integral: a " cos(2) dy dar.

A: The iterated integral is given as:…

Q: Consider the integral sin(5z) d: Applying the integration by parts technique, let and du x dz Then…

A: The by parts formula of integration is ∫udv=uv-∫vdu.

Q: Evaluate the integral da 2+ et using the substitution u = 2+ eª. dx 2+ et +C | -

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Q: Evaluate the integrals in Exercises using integration by parts. 3. f cos t dt 4. * sin x dx

A: The formula for an integral ∫udv is uv-∫vdu. Here u function is selected on basis of ILATE order.…

Q: Evaluate the integral 24 11) dx, by making the appropriate substitution: u = Ja* (2* – 11)*“dz =

A: ∫ un du =un+1n+1+C

Q: Write the integral in terms of u and du. Then evaluate. (6x + 19)-2 dx, u = 6x + 19

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Q: Evaluate the integral 20 | by making the appropriate substitution: u = 5 – 2 (2³ – 2)® dx %3D -

A: Evaluate the integrals

Q: What is the integral of fcos (2t)dt? COS

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Q: Evaluate the integrals in Exercises 2. J 3 dx dx 1. 9 + x VI + 9x

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Q: Evaluate the integral. xp- sin? 3x 15) -In |sin 3x|+ C B) - 1x cot 3x +1 In |sin 3x| + C 3 A)1x cot…

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Q: Evaluate the integral. |a cos(6 z) dz =| %3D

A: Topic:- integration

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 indicated substitution to evaluate the integral.

A: we have to use the substitution x=3secθ to evaluate the integral ∫dxxx2-9

Q: Evaluate the integral using the given substitution. 5- sin cos dt, u= 5- sin- cos 1 O A. 5- sin 3 t…

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Q: -3v3 dx V9+x?

A: Evaluate the intregal

Q: Evaluate the integral using the given substitution. Jx cos (5x?) dx, u=5x? O A. sin (5x2) +c 1 O B.…

A: Note:Since you have asked multiple question, as per our guidelines we are supposed to answer only…

Q: Evaluate the double integral. Sxy² da, D is enclosed by x = 0 and x =

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Q: Evaluate the integral dx (4x + 14) by making the appropriate substitution: u = dæ (4x + 14)* Submit…

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Q: Evaluate the integral cosx dx from í/3 to π/2 * 0.134 0.500 0.293 0.707

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Q: Evaluate the integral. * T/2 sin³x cos y dx

A: Using identity         Sin2x+cos2x=1

Q: Consider the integral 7x – 21 da 2x – 3 If the integral is divergent, type an upper-case "D".…

A: the given integral is ∫027x-212x-3dx

Q: Evaluate the improper integrals in Exercises •3 dx 53. 54. In x dx V9 dy de (0 + 1)3/5 56. 55. (y –…

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

Q: Which among the following is an improper integral? 0.5 dx a. -0.5 1-x2 csc?x b. Ji V5-csc2, dx…

A: (a) The integral given in (a) has a finite value. Therefore this integral is proper. (b) The…

Q: x2 dx 3. (бх2—49)"/2 49 [V36x3-9x IVox + v6x2 –9 + In + C I 12v6 49 7

A: In this question we will use basic of calculus i.e concept of integration. We will simply use…

Q: Evaluate the integral. e sec²(8x) dx %3D +C

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Q: Compute the integral using contour integration: 27 cos no (cos 0+a)20 for a > 1.

A: Note:- ∫C fz dz =2πi ×sum of residues cosnθ= Re ei nθ  cosθ=ei θ+e-i θ2      Given that  ∫02π…

Q: Evaluate the integral. sec3xdx A In sec3x+ tan3x+c There is no correct answer from the given…

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Q: e In (x le) (2- secx dx to be integrable using the formula - se What should be the value of A for u"…

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Q: What is the integral of f 2z²–3z+2 1 -dx? O vi tan () +C 7 O None of the choices Gan '(녹루) + C 4z 3…

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Q: Use the Residue Theorem to evaluate the a? integral dx + x2 where a>0

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Q: Evaluate the following integral: J Sec?x -dx V1-tan2X

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Q: (24 — бх) dx 14

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Q: Evaluate the integral (use the substitution) : 2x + 6 x2 + 6x + 13 dx а. In (x + 6x + 13) + C b. 1…

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Q: The result of the integral in 0 given V Vr²- 25 -dy is 5 tan0 -50 +C, True B False

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Q: Consider the integral sin-'(5x) dæ: Applying the integration by parts technique, let U = and dv dx…

A: Integration by parts is expressed as If I=∫f(x)⋅g(x)dxThen I=f(x)∫g(x)dx  - ∫ddxf(x)⋅∫g(x)dxdx Here,…

Q: Evaluate the integral fos√²²-1 f√²-1. 2x by first rewriting in the order dxdy. Enter the numerical…

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Q: Use residues to evaluate the integral 2T 1 de. %3D 5+3 cos 0

A: To evaluate : ∫02π15+3 cos θdθConsider unit circle |z|=1i.e. z=eiθ⇒dθ=dzizAlso, we use cos θ=z2+12z,…

Q: Use a double integral to find the area of the shaded region. -3 -1 π/2 -3 r = 2 cos 20 3

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Q: dx, Evaluate the improper integral : [° 6x³e-3x°

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