•4 x dx 10 x2 – 9

Q: Determine whether the improper integral diverges or converges. Evaluate the integral if it…

A: To evaluate the integral∫0∞x3(x2+1)2dx

Q: Evaluate the integral if it converges or show that it diverges: integral 1 to 9 1/(√x−3)dx.

A: Given that : 1/(√x - 3)  evaluate the integral between 1 to 9. And also check it is converges or…

Q: 9x Determine if the improper integral | dx converges or diverges. If it 2 converges evaluate the…

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Q: 1 Prove that the integral : Tz dx is convergent. 1+x

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Q: dx (x– 1)%

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Q: Determine whether the improper integral diverges or converges. dx 1. (2х-1)3 dx 2. x +1

A: No.2 The improper integral is of second kind where f(x) = 1/(x+1) has one point of infinte…

Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answe dx = (x +…

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Q: dx 0, бх + 1

A: We have to check whether the given integral is converges or diverges.…

Q: Determine whether the improper integral converges or diverges. Fnd the value if it converges.…

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Q: Determine whether the integral converges or diverges; if it converges, evaluate. dx Зх — 4

A: In the given question there is an integral given and we have to find whether it is convergent or…

Q: Determine whether the improper integral diverges or converges. 0. -5x хе dx

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Q: Determine whether the integral is convergent or divergent. x arctan(x) 63 dx (1 + x2)2

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Q: Determine whether the improper integral diverges or converges. dx 1. (2x-1)3 7 dx 2. -1* + 1

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Q: Determine if the integral x In x dx converges or diverges. If it converges, compute its value.

A: The given integral is ∫01xlnxdx.

Q: Determine whether the integral is convergent or divergent. '3 29 dx V3 - x O convergent O divergent

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Q: Determine whether the improper integral converges or diverges. V5x + 8 dx x2 1

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Q: Determine whether the improper integral converges or diverges

A: Given integral is, ∫0∞x4e-xdx

Q: Determine whether the integral is convergent or divergent. 1 dx x² + x

A: a) limt→∞∫6t1x2+xdx=limt→∞∫6t1xx+1dx Use partial fraction 1xx+1=1x-1x+1

Q: Determine whether the improper integral converges or diverges

A: Given: ∫1∞1-sin(x)x2 dx We have to check whether the improper integral converges or diverges

Q: Evaluate the integral if it converges and enter the exact value. If the integral diverges, indicate…

A: Given; I=∫0+∞6dxxx+1  ...1 Apply the substitution method to solve the given integral. Let,…

Q: Determine whether the improper integral or is divergent. S 1 1+2* +e²x dx is convergent

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Q: Determine whether integral 0 to pie /2 sec x dx    converges or diverges

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Q: 1 dx 7x° +9x x² +3 dx 2 2x* +x

A: Explanation of the answer is as follows

Q: Determine whether the integral  integral  1 to infinity (1/x) dx is convergent or divergent

A: We will use the fact that

Q: Explain why the improper integral (x + 3) sin(x) dx L. (x² + 1)(x² + 4)² is convergent. 8

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Q: Determine whether the improper integral diverges or converges. Evaluate the integral if it…

A: Here given integration as I=∫2∞1xx2-4 Since ∫1xx2-a2=1asec-1xa+C

Q: Determine whether the integral is convergent or divergent. x arctan(x) 00 11 dx (1 + x2)² convergent…

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Q: Determine whether the improper integral diverges or converges. x In(x) dx converges O diverges

A: Given: ∫01x3ln(x)dx

Q: use the Comparison Test to determine whether or not the integral converges.

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Q: Determine whether the integral is convergent or divergent. `"e-1/x dx convergent divergent

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Q: Determine whether the integral is convergent or divergent. 6. 8 dx x- 1 3 convergent O divergent If…

A: The given integral is: ∫098x - 13dx We have to check that the given integral is convergent or…

Q: Show that the integral is either Convergent or Divergent. If it is convergent evaluate the integral.…

A: To determine the value of the integral.

Q: 4. (a) Explain why the integral (1+ x)3 dx is an improper integral. Determine whether the improper…

A: We have to find out

Q: Determine whether the integral is convergent or divergent. *e-1/x dx x2

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Q: Determine whether the integral is convergent or divergent. x arctan(x) 00 11 dx (1 + x2)2 convergent…

A: Given integral, I=∫0∞11xtan-1x1+x22dx Used formulas, ddxtan-1x=11+x2ddxx=1…

Q: Determine whether the improper integral diverges or converges. Evaluate the integral if it…

A: Definition used-        Integral is convergent if the limit exists and a finite number,…

Q: or show that it is divergent Evaluate the integral dx 10

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Q: .2 x+15 dx Jx* +3 1

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Q: Determine whether the improper integral diverges or converges. -6X dx xe converges O diverges

A: Given, ∫-∞0xe-6xdx

Q: 2. Determine whether each improper integral is convergent or divergent. Justify your answer. L dx.…

A: We need to determine if series converges or diverges.

Q: 0 1 -dx 1 1. 1 dx 1 (3x+1)² 2.

A: Determine whether the following improper integrals are convergent or not.

Q: Determine if this improper integral will diverge or converge dx (x² – 1)4/3 1 Apply this in solving:…

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Q: Evaluate the integral if it converges and enter the exact value. If the integral diverges, indicate…

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Q: b) Determine whether the improper integral `1+ sin r -dx 1+x² converges or diverges.

A: Comparison test :  Suppose for x>a  . If converges then also converges . If diverges then…

Q: dx .1 ех — 1

A:

Q: Evaluate the improper integral and state whether it converges or diverges.

A: Definite integral convergence

Q: Evaluate the improper integral if it is convergent. (If it is divergent, type DIVERGENT 7e e-x/2 dx…

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Q: 8. Determine if the improper integral is convergent 00 -3x dx 6 e xp,

A: Given integral is   ∫0∞6e-3xdx Then  ∫0∞6e-3xdx = 6∫0∞e-3xdx = 6e-3x-30∞=-2e-∞-e0=-2(0-1)=2 ⇒…

Q: 9) Determine whether the improper integral diverges or converges: 0o 4 dx

A: Evaluate the integral, if it has a real value, it converges.

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.