1. For each of the following, compute the integral by u-substitution. Make sure to explain your choice of u and du, and show your work to explain your reasoning. (a) ſ´ 2r(x² + 2021)av22 dr (b) S 3r² cos(r* – 4) dr

Q: 3.Evaluate the following integrals by any method of your choice S(1+) ) dt a. 6x2 b. (4х3 - 9)3

A: We have to find integral

Q: Consider the following integral. fx²√³+1 dx Identify the definite integral that will result after…

A: topic- indefinite integral

Q: 2. Each of the following integrals requires U-substitution to evaluate. Rewrite the following…

A: Topic- Integration

Q: Which of the following integrals is equal to (3x-5) dr if u=3x-7? (A (u+2) du 8/3 -2 -1 / (u-2) du…

A:

Q: 1. Evaluate the following indefinite integrals: S(72³ – 2.a²)(5x – 3)dx а. b. S SVE-7# dx d.x

A:

Q: 10. Evaluaté the following integrals (b) J3 -6a+13 1 (a) S x²+1 -0 x4+1 ;d.x

A: We can solve this using partial decomposition and using integral

Q: 4. Evaluate the following integrals cos 3x - dx а) (x² +4)² do b) 5-4cos0

A:

Q: Evaluate the following integrals: S cos“ : x dx 1-

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

Q: - Evaluate the following integrals 2e**+11e3x+16e2x -dx e2x+5ex+6

A:

Q: 20 In evaluating x(2x+5)8dx you use the u-substitution u=2x+5. After doing that, which of the…

A:

Q: 3. Which of the following integrals cannot be evaluated using a simple substitution? 1 xp- x +1 ,4 1…

A:

Q: 1) Evaluate the following integrals a. - 1)6(t)dt

A:

Q: For 1/2 U -dx and using the substitution -du -du 4u √4-(2u²) ² 4u du -du 1/2, the resulting integral…

A: In this question, we want to know the Integral form after substitution.

Q: Evaluate the following integrals.

A: To evaluate the integral: ∫-11ww2+13dw Solution: Property of definite integral states that:…

Q: 1. Evaluate the following integrals * () dr cos (b) e cos 2r dr (c) +1-2 dr r2 +x - 2

A:

Q: 3T en: S 5x² cos 3x³dx. If u = 3x³, then the resulting integral is S f(u)du. Find f (").

A: Given query is to find the indicated function.

Q: 4. Use residue theory to calculate the following integrals: 3x (a) P.V. · Loo (2²+49) (2² - 2x + 5)²…

A:

Q: Evaluate the following definite integral ,-(s-2)t sin(3t) dt. 3 2 (8 – 2)2 + 9 (8 – 3)2 + 4 - - O 1.…

A: Properties of Laplace transform  Lf(t)=∫0∞e-stf(t)dt Leatsinbt=b(s-a)2+b2 Lsinat=as2+a2

Q: 12 Which of the following is an integral of the function: f(x) = e2x ? %3D et e2x O 2ex O 22x O…

A: Given function is fx=e2x We have to find the integral of this function.

Q: 1. Find the following indefinite integrals: 1 du b. fcos uchu = а. 1 fa'du- d. . du - с. 1+u? f. f-…

A:

Q: Make the given substitution to evaluate the indefinite integral. 28r dr .u= 3-r 3-r'

A:

Q: In evaluating / (2r+3) V+2, by substitution, if 4=x+2 then what will be the resulting indefinite…

A:

Q: Find the following indefinite integrals if a, b and c are positive real numbers, with a +-1 and b +…

A: Note that a≠-1 and b≠ 1    then we can solve these integral

Q: (2) Compute the following integrals. /4 (a) sin (4r) cos (4.r) dæ. (b) cos(ka)e-lz dx, Hint:…

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Q: 3. Evaluate the following integrals (a) S(x² + 2x – 4) dæ

A: If Fx is a particular antiderivative of a function fx on an interval ?, then every antiderivative…

Q: 1. Evaluate the following integrals. Show all steps! 2 x + 3 dx x(x – 3) 1? — 4x + 6 - dx (b) | (x –…

A:

Q: The result of the following double integral is 2 SS T oxy²z dxdzdy = ? -2°0 None of he others O -21…

A:

Q: If f(x)= the definitive integral from 3 to x of (t2+5)1/2dt, find f'(5).

A: Given : fx = ∫3xt2+5

Q: In evaluating (2r+3)Vx+ 2 dx by substitution, if 4=x+2 then what will be the resulting indefinite…

A: This can be evaluated as follows:

Q: We now use the substitution u = x° + 8x and du = (9x° + 8) dx to convert the entire integral into…

A: We have to solve integration

Q: 1. Find the following indefinite integrals: a. G b. fcosudu = 1 c fa'du=- d. Jitu du = e. fsecu…

A:

Q: In evaluating | x(4 – x)3dx , if we use the substitution that u = 4 – x, then what will be the…

A: Indefinite Integration using substitution

Q: (b) S *+2=-3dx

A:

Q: - Find the reduction formula for each of the following integrals i. In = S cot"x dx, then find I4

A: Use the Trigonometric identities and reduced the integral.

Q: Evaluate the definite integral. 2 St³√₁+t² dt 0

A:

Q: Use residue theory to calculate the following integrals: 3x 1. Loo (x² + 49) (x² − 2x+5) (a) P.V. dx

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: 1. Use substitution to express each of the following integrals as a multiple of Sadu for some a and…

A:

Q: Q1 - Find the reduction formula for each of the following integrals iii. In = S x" cosh2x dx

A:

Q: 1) Find the indefinite integral of the following functions: 3 2x+ 3x4 a) y = Axt B 3 b) y =x-1 +…

A: Indefinite Integration

Q: 1. Evaluate each of the following integrals. Show all work. 7/5 (a) 2 cos(5æ) dr (b) 3 dt 4+ 5t

A:

Q: Solve the following integrals: S(2cos2(x)) dx using the substitution of cos(2x) = 2cos²(x) – 1.

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Q: The result of the following double integral is 2 2 у ST (6 x² y - 5 e)dxdy= ? 0. -2 y 909 -20e? +…

A:

Q: 1. Evaluate the following integrals. Do not simplify! (a) S 7x(3x² + 5)'14dx

A: Given that a)∫7x(3x2+5)14dx b)∫x-3x+8dxc)∫x(4x-1)6dxWe need to evaluate the integral

Q: Evaluate the following integral from a=-0.4 to b=7.6 with single application of Simpson's 1/3 rule b…

A: The solution is given as

Q: Evaluate the following Integral by using suitable method S(e-4YV1+ e-4y 2y3+y dy y4+y2+1/

A:

Q: 2 s² +V5 ds 2.1 s2 V3 L(t + 1)(t2 + 4) dt 2.2

A:

Q: For the following integral: f3ae-2 dx

A: NOTE: Refresh your page if you can't see any equations. . use the integration by parts method so…

Q: 3. Which of the following is an improper integral? -dr -4 x²–x- 2 А. In3e COSX хе 'dr В. dx c. 2x+ 8…

A: Given problem:-

Q: 1. Evaluate the integral using the given substitution xcos(9x2)dx u = 9x2

A:

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.