dx 1 x In x

Q: For the following integral, prove that it converges or that it diverges. I sin(e') dt

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Q: The integral Jo x°dx converges when a < 0 True False

A: Given integral is ∫0∞xαdx with α≤0 we check the value of integral for α≤0

Q: e dx (1– e*)2

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Q: determine whether the improper integral converges and, if so, evaluate it.

A: We write the given integral using limit k approaching infinity

Q: 1 dx, \x| < 3 (a) -x? – 2x+8 In x dx (b) Jx

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Q: 1 1 dx

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Q: x³ + 2x² + 3 4/9 dx 3x6 + 17x10 + 10x12 8°

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Q: Determine if the integral converges or diverges. If it converges, give its value. re+3 1 dx 2 (3-…

A: Let us consider the given integral I as: I=∫2e+313-xln3-xdx Let us make substitution by putting…

Q: For what value of c does the integral converge? Evaluate the integral for this value of c.

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Q: Determine whether the following integral converges or diverges. a) 6.00 ㅠ b) fo X (x² + 1)² tan x…

A: Let us determine whether the integral converges or diverges in the next steps.

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

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

Q: Evaluate the following Improper Integral. Does the limit converge? Why or why not? 1 dx xIn x

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Q: Does the following integral converge or diverge? Justify your answer. 112 dx Vx*+13

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Q: Determine whether the following integral converges or diverges a) L. 3 dr, 4 – 2x b) / dr. /8 -

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Q: Evaluate the following improper integral if it is convergent. 00 10 dx x In x Select the correct…

A: Given information:          The integral is ∫2∞10x ln xdx  Calculation: The integral will converge…

Q: Evaluate the following improper integrals by finding where the integral converges to or if it…

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

Q: Evaluate the following integral if it converges: 1 dx

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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: Compute the value of the following improper integral. If it converges, enter its value. Enter…

A: The given integral is: I=∫2∞dx(2x-2)2 Substitute 2x-2=u⇒2dx=du⇒dx=du2As x→2⇒u→2as x→∞⇒u→∞ Therefore,…

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: For what real numbers p does the improper integral epa dx converge? Find the value of the integral…

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Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answer. dx = %3D…

A: Given that, ∫-∞1e2x1+e2xdx Let,  u=1+e2xdu=2e2xdx For x=-∞, u=1+e2(∞)=1+0=1

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

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Q: Determine whether the improper integral converges and, if so, evaluate it.

A: ∫1∞dxx20/19

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: | sin(e') dt

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Q: 53. In x dx

A: Solve the following integral

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

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Q: Determine whether improper integral converges or diverges, and find the value of each that…

A: To determine whether improper integral converges or diverges and find the value of each that…

Q: d.f* .3 e x* dx

A: The given improper integral is: ∫0∞ e-x3 dx

Q: Which of the following integrals converge? If they converge, evaluate them. (a) | x log(a) dx, (b)…

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Q: Determine the values of p and q for which the integral below converges. dr 1* (In z)"

A: Given: ∫12dxxqln xP

Q: 1 dx (r-2)2 а.

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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: For what values of is the following integral convergent 1 to infinity 1 / xp  dx

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Q: determine whether the improper integral converges and, if so, evaluate it.

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Q: Determine the convergence of each of the following integrals by comparison with the given integral.…

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Q: The following improper integral f,"(x? + 1)e¬*+²dx +2, converges to e

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Q: 1 dx V16 – x²

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Q: Each of the following definite integrals are improper. Determine which converge and which diverge.…

A: We have to evaluate the improper integrals ∫0∞ 11+x2 dx ∫02 x4-x2 dx ∫1∞ ln(x)x dx

Q: 3x 1. dx (Зx2 + 2)2 -3 2.J2 13-x 1 dx

A: Convergence of the series

Q: -0.1x dx e 1 8.

A: We use integration of e^x dx =e^x.

Q: Determine whether the integral given below converges or diverges. dx 1 ve* – x

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Q: For the following improper integral, determine whether it converges, and determine its value if it…

A: Let us first find ∫  e-xee-xdx. So,               ∫ e-xee-xdxLet u=e-x=∫ -eudu=-euSubstitute back…

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

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Q: dx o (x–1)? 2.

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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: Evaluate the following integral or show that it is divergent. 0 -√x VX dx

A: Explanation of the answer is as follows

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.