³ + 2x² + 3 4/9 dx 3x6 + 17x10 + 10x12

Q: .1 1 dx Jo 0/ V

A:

Q: (b) dx (1+ x²)² 0,

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Q: The following improper integral ,dx x²-9 converges to –V15 diverges to -∞ This option O This option…

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Q: 1. S(In x)² dx

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Q: Consider the integral 7x dæ 1+ x? 00 If the integral is divergent, type an upper-case "D".…

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Q: State whether the following integral is Convergent or Divergent. e*dx 8. O Convergent O Divergent

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Q: dx 4. S 25 – 16x²

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Q: Determine if the following integrals converge or diverge by using the indicated tests next to them.…

A: According to the given information it is required to determine whether the integrals in each part…

Q: Evaluate the following IMPROPER INTEGRALS, It is optional to double check your answers/solution for…

A:

Q: +00 dx d.x (1+x)/x

A: Given: To show: The given integral converges.

Q: 1. x +4 √x -dx

A: We will use substitution method.

Q: Q1/ Use Gauss-Legendre formula to evaluate the integral o e-dx withn= 3.

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

Q: 4. dx +

A:

Q: Which of the following integrals converges? S а. 1+x 0.1 b. dx 1+x с. dx 1+x 01 dx 1+x0.1 d. е.…

A: We use the fact given in the image to identify the convergence of integral.      Ans-(a)

Q: 2. dx 1+√√x

A: integration

Q: sin (x), dx b) J∞ 4+x²

A: Given improper integral: ∫-∞∞sinx4+x2dx Let x2=4tan2θ         x=2tanθdx=2sec2θdθ Substituting these…

Q: Determine if the following improper integrals converge or diverge. If they converge, find their…

A: The answer is given as follows.

Q: Evaluate the following integrals by first reversing the order of integration. 8 2 √° ²₂ √² + 1 dr dy…

A: Given Integral, I =∫08∫y1/32x4+1dxdy and the region of integration is, 0≤y≤8 ,y1/3≤x≤2 Graphically…

Q: Vhich of the following integrals is equal to the integral f(3x - 5) dr?

A: Use simple integration concept.

Q: Determine if the following improper integrals converge or diverge dx 2) 1 + e-2x -8

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Q: 4. Use the comparison property to calculate if the following integral converge: sin? a dx. V1+x3

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Q: 4. Use the comparison property to calculate if the following integral converge: sin? x dx. | 1+

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Q: Evaluate the following improper integrals, where the integrand is unbounded, if they converge, or…

A: Given improper integrals . To evaluate the given integrals , where the integrand is unbounded if…

Q: 5.) / a In a dx

A: Given, ∫x3lnxdx  Using Integration By Parts, ∫u dv=uv-∫v du Here u=ln(x), dv=x3…

Q: Evaluate the following integral by using substitution ∫4x/√(x^2+1) dx   limit: 0 to √48

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Q: Does the following integral converge or diverge? Show all steps 1 (x – 1)4/3 dx

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Q: Evaluate the following integral or state that it diverges. 8 -dx 3 7 (x- 7)2 Select the correct…

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Q: Which of the following improper integrals are finite and well- defined? (Tick all that apply) /2 O…

A: some improper integrals are given, we have to find finite and well defined

Q: Which of the following integrals is convergent? Select the correct answers. .24 0 of OP 0 2 X dx dx…

A: We have to find which of the following integral is convergent. (a).…

Q: 34) Which of the following improper integrals converge? roo 1 -dx x In(x) a) 1 æ(In(x))?dx cos(x) c)…

A: We are only allowed to solve one question at a time and up to three sub-parts. So, we will answer…

Q: Evaluate the following indefinite integrals: S (5.x2 – 3x)(2x + 4)dx а.

A:

Q: Evaluate the following integral using the summation rules. 9. (6 + 6x – x²)dx

A: Consider the following definite integral: ∫096+6x-x2dx Apply summation rule:…

Q: 4. ſ sec*xtan3xdx 5. ſ cot³xcsc³x dx

A:

Q: Evaluate the integral using the following values. 6 6 6 fox Lº Sº dx 4 4 x3 dx = 260, x dx = 6 [²…

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Q: Find the following, using no tables for any non-basic integrals. [31evoz d Did you remember your +C?…

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Q: Evaluate the following integral using Romberg's method by taking n =8: 'dx

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Q: Evaluate the following improper integrals whenever they are convergent. а. 1 b. (2.x+3)* 00 1 :dx V1…

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Q: Does the following integral converge or diverge? Justify your answer. 112 dx /x°+13 8

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Q: Approximate the following integral with n = 4 using trapezoidal rule. 2 dx |x|Vx² – 1 1.5

A: The trapezoidal rule uses trapezoids to approximate the area. The formula below is used to evaluate…

Q: etermine the following integrals by using (IF) 1. S dx 4x2+4x+1

A: Topic:- integration

Q: 1 dx V16 – x²

A:

Q: Using Simpson's 3/8th rule, evaluate the following integral with 6 sub-intervals -2 (x+1)dx Jo…

A: The given integral is ∫02x+1dxx2+2x+2 We will evaluate the integral using Simpson's 3/8th rule with…

Q: Use the Comparison Theorem to determine whether the following integral is convergent or divergent. 4…

A:

Q: Which of the following improper integrals converge? Justify your answers. I e* sin(e") dz 1. sin()…

A: 1. The given integral is ∫0∞ ex sinex dx. This implies that, ∫0∞ ex sinex dx=∫0∞  sinex…

Q: For what values of  a is ∫0∞ eax cos x dx convergent? Evaluatethe integral for those values of a?

A: ∫0∞eaxcosx dx Now, ∫0∞eaxcosx dx=limt→∞∫0teaxcosx dx=limt→∞eaxa2+1acosx+sinx0t    ∵∫eaxcosbx…

Q: Compute the following integrals: et? + + 4 2x ex? + 4x2 + x 1. - dx

A: Solution of this question is

Q: Determine whether the integrals below converge or not. Do not try to evaluate them. (a) dx 1 d.x 1…

A: As per the question, we need to determine whether the given integrals converge or not without…

Q: Find the following improper integrals and then state whether it converges or diverges. a) S," In…

A: The  improper integral is given as ∫1∞lnx2dx To find : whether the given  integral converges or…

Q: Which one of the four integrals below has a finite value ? Select one: 00 x? dx 00 1 dx 3 00 x dx 3…

A: We have to find the integral which have finite value.

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.