Consider the indefinite integral Je+ 7x+4 dx: a) This can be transformed into a basic integral by letting и 3 Preview and du Preview b) Performing the substitution yields the integral Preview c) Once we integrate and substitute, the final answer in terms of x is:

Q: Make the given substitution to evaluate the indefinite integral. 7(7x+ 14) dx, u= 7x+ 14 %3D

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Q: Evaluate the integral using FTC I.

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

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Q: 2Sin Cze) 4-COS S (zt)

A: The solution for the above question is as shown below.

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 integral using Part 1 of the Fundamental Theorem of Calculus. 4x(1 – x² )dx = i

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Q: Evaluate the integral using FTC I.

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Q: O Calculate He in tegual usng the Caucly Integral Theoren sin b (2) dz

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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: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 5 4x(1 – x² )dx = i

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Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. | 4x(1 – x² )dx = i -1

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Q: Find the exact value of the integral using formulas from geometry. 5 (3+ 2x)dx 1

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Q: Evaluate the integrals in Exercises using integration by parts

A: We know that, Integration by Parts is a special method of integration that is often useful when two…

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: S tan-3 (x) sec² x dx

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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: Using appropriate substitution, the integral *+imx) dx is equal to: an

A: From the given problem:   I=∫141+lnx3xdx...1   Substitute in equation (1).   1+lnx=u...Differentiate…

Q: Evaluate the integrals in Exercises

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

Q: Evaluate the integrals in Exercises: -1/3 6 dx VI + 9x? 5- TT cos x dx Jo vī + sin²x Vi + sin²x 6-…

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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: sec(2) tan(z) – 1 dz 1 dz

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Q: Evaluate the integrals in Exercises 51–56 by making a substitution (possibly trigonometric) and then…

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Q: Using only the definition of RS-integral, evaluate 2 ,2 x* d[x}.

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Q: The value of the integral (17 tan z- 17 sec r)dr = %3D O -68 O 4 O 68 O-4

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Q: Evaluate the integral using FTC I.

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Q: Evaluate the integrals in Exercises using integration by parts.

A: Integration of a function is the process of finding the anti-derivative of the function. The…

Q: Evaluate the integrals in Exercises using integration by parts

A: Since you have posted more than one question, we answer the first question for you. For the other…

Q: Evaluate the integral (1+ etane) Sec?0 de

A: The given integral is, I=∫0π41+etanθsec2θdθ Let us solve the given definite integral using the…

Q: Use the given substitution to evaluate the integral.

A: Given integral: ∫sec22θ tan2θ dθ

Q: In Exercises 43–47, calculate the integral, assuming that f(x) dx = 5, g(x) dx = 12 %3|

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Q: Evaluate double integral 0 to 2, x to 2 2y^2 sinxy dydx

A: We have to integrate the double integral:

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 using the methods covered in the text so far.

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Q: Evaluate the integrals in Exercises 45. tanh dx 46. coth de

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

Q: Evaluate the integral: + 6 dx = %3D

A: Find the integral by using substitution method

Q: sin 4zdz J 16+ sin ª 2= 4.

A: The given function is sin 4z16+sin4 2z We have to evaluate the integral of this function.

Q: Calculate by using integration by substitution, Sec V11 tan15 da What was yoOur substitution? What…

A: Given that ∫sec2x11tan15x11dx find out the integral by substitution

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 4 4x(1 – x²)dx = i -1

A: To find the value of given integral.

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: Compute the defined integral So [1+ e* sin(4x)] dx using the trapezoidal method with two segments.…

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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: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 5 | 4x(1 – x² )dx = -1 i

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Q: Use the substitution formula to evaluate the integral. the integral from 0 to pie/2…

A: To  Determine:Use the substitution formula to evaluate the integral. Given: we have an integral…

Q: (24 — бх) dx 14

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Q: Is the integral / A · dr path independent if A = (2x - y)i+ (x + y)j? of Evaluate A · dr around a…

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Q: evaluate the integral using substitution method sin√w/√w dw

A: The given integral beI. I=∫sinwwdw. The most important step is to convert  variable such that the…

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: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 2 | 4x(1 – x² )dx = i -1

A: Given,    ∫-124x(1-x2)dx