Evaluate the integral by making the given substitution. xV+ 14 dx + 14 dx, u = x3 + 14

Q: Evaluate the integral | a (2° – 5)26 dx, by making the substitution u = x6 - 5. +C Note: Your answer…

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Q: Write the integral in terms of u and du. Then evaluate:  ∫ (x − 7)3 dx, u = x − 7

A: ∫x-73 dx Put, u=x-7⇒dudx=1-0⇒du=dx Therefore, ∫x-73 dx=∫u3 du

Q: 4 dx, u= 1 + 2x (1 + 2x)

A: Explanation: Given that: ∫41+2x3dx,      u=1+2x Concept: 1. ∫xndx=1n+1xn+1+C Calculation: First…

Q: Use the substitution formula to evaluate the integral. S'ia dx (Hint: simplify first) 1 2 11 22

A: Solve the following

Q: Evaluate the integral. 17 dx 2 Vx² – 1 - NOTE: Enter the exact, fully simplified answer.

A: Let's find.

Q: Evaluate the integral a* (a* – 4)"da - by making the substitution u = x* – 4. + C NOTE: Your answer…

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Q: dx Evaluate the given integral: Jo 5-ex

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Q: Evaluate the integral: ſo (x³ – 5æ + 7)dx. Select one: O None. 19

A: Given :∫01(x3-5x+7)dx

Q: Evaluate the integral by making the given substitution. dx u = 7x + 8 (7x + 8) '

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Q: Evaluate the integral. T/2 9 cos?(0) de

A: Integration of 9 cos2(theta) from limit 0 to π/2.

Q: Evaluate the integral 18 - 6)"da, by making the appropriate substitution: u = *(=* - 6)*dx = 18…

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Q: Evaluate the integral: So " (10 + 2z? + 2y²)dx dy. 160 3. 100 3. 110 3. None of these. 140 3

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Q: a. ²₁ (5x¹-2x³) dx

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Q: 1 dx J Vx² + 2x + 5

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Q: Evaluate the improper integral: 9. dx a) Odiverges b) О 18 c) 09 d) 03 8.

A: Given integral :

Q: (a) Evaluate the integral using the substitution u = In (5x). x In (5x) dx x In (5x) ? Edit +C (b)…

A: An integral in some cases can be simplified using a substitution. For example ∫ln(x)xdx with the…

Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

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Q: Evaluate the integral |x'(x* – 7)6 dx, by making the substitution u = x* – 7. +C Note: Your answer…

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Q: Evaluate the integral J 2x(x² + 6)¨ dx using the substitution u = x2 + 6. | 20 (a? + 6) " d.x +C

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Q: Evaluate the integral * (2* – 8)* dz, 33 by making the appropriate substitution: u = 33 NOTE: Your…

A: We need to evaluate the following integral I = ∫x3x4-833dx                         ..........1…

Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

A: Given : Integral  ∫ex-21x-21dx   To find : Evaluate the given integral by using u-substitution?

Q: Evaluate the integral by making the given substitution. dx u = 7x + 4 (7x + 4)3 + C

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

A: 27. Given integral is, ∫x3+x+1x2+12dx.   It is integrated as follows:

Q: Find or evaluate the integral by completing the square. (Use C for the constant of integratiOn.) x4…

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Q: dx What is the result of integral ? le xln³x A) B) o C) D) – o

A: Use the substitution for Lnx=v

Q: Find or evaluate the integral by completing the square. (Use C for the constant of integration.) dx…

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Q: Evaluate the integral 45 1)" da, by making the appropriate substitution: u = 45 dx =

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Q: Match each integral and its substituted form with the proper substitution. |(15x -10)3x²-4x+11 dx…

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Q: Evaluate the integral by making the given substitution. dx u = 3x + 9 (3x + 9)3 + C

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Q: What u-substitution should be made in order to evaluate the following integral? dx (6x² + 4)* u =

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Q: Write the integral in terms of u and du. Then evaluate.

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Q: Evaluate the integral. a dx 2 a > 0 (a² + x²)3/2' V2 92

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Q: Use the substitution formula to evaluate the integral. dx 1. 22 11 11 O00

A: Solving the problem by substitute method.

Q: Evaluate the integral. x sec?(8x) da +C

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Q: 3x?-13х+14 dx 36х2-72х

A: Topic:- integration

Q: Evaluate the given integrals. 4. J(secx + tanх)? dx

A: Given problem:- ∫ (tan(x) +sec(x))2 dx

Q: Evaluate the integral 29 (2° – 2) dx -y making the substitution u = x° – 2. + C NOTE: Your answer…

A: Given query is to find the integral.

Q: Write the integral in terms of u and du. Then evaluate. xV9x + 4 dx, u = 9x +4 (Use symbolic…

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Q: Evaluate the integral. 19 dx x²Væ² – I NOTE: Enter the exact., fully simplified answer.

A: To evaluate:∫2219x2x2-1dx

Q: Evaluate the integral 17 a* (x* – 3)"dæ by making the substitution u = x* – 3. +C NOTE: Your answer…

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Q: 11 dx Evaluate the integral: , (5æ+6)² 11 55

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Q: Evaluate the integral and choose the correct answer. fxe² dx O Ọ xe ttc o xe etc Ọ - xẻ +C xe - 2e +…

A: Topic = Integration

Q: Evaluate the integral. 13 dx 1 O A. 0 О В. - 13 13 Oc. -ze? O D. 13

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Q: Write the integral in terms of u and du. Then evaluate. | 8xe* dx, u = x2 (Use symbolic notation and…

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Q: Evaluate the integral by making the given substitution. (5x)tan(5x)dx, u = 5x + C

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Q: x2 dx Vx? – 4x + 5

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Q: Use the substitution formula to evaluate the integral. T/20 (1.clan 5x) sec2 5x dx Select one: O A -…

A: Substitute the trigonometric function in some other variables.

Q: Evaluate the integral: , (x2 + 3x)² (2x + 3) dx Choose the most appropriate answer. -464.67 O 81.67…

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Q: Watch the video on a u-substitution followed by a this question. To start the integral a V1+x6 dx,…

A: Given problem is : Solution : We use substitution to simplify the integral.

Q: Evaluate the integral *(2 – 6)"dz 10 - by making the substitution u = x° - 6. + C NOTE: Your answer…

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.