6. The improper integral 1 dx converges to х -5 попe 2 1 4

Q: (b) Prove that the improper integral Ï Ï -8 -∞ converges. dx dy (1 + x² + y2)3/2

A: Consider the given improper integral, I=∫-∞∞∫-∞∞dxdy1+x2+y232 Change into circular coordinates by…

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

A:

Q: et Determine if the improper integral dx converges or diverges. (1 - e)2 If it converges, find its…

A:

Q: The improper integral -dx is (x+2)® 1 converges to O Diverges converges to converges to converges to…

A: ∫-1∞1x+295dx=∫-1∞x+2-95dx                                =-541x+245-1∞…

Q: In S₁² = 10 A (1,00) B (-∞0,00) c) (-∞,1] D {0,1} Given -dx, determine all value/values of P for…

A:

Q: 2- Find the values of p for which integral converges. dz z(ln z)

A:

Q: The improper integral | 1 -dx is (x+2)9 O None Diverges converges to 5 converges to converges to 5…

A:

Q: 6. Is the following improper integral convergent? There is no need to compute the answer, but you…

A:

Q: 1 (a) Use the Integral Test to show that > converges. 2. n' +1 d 1 n = 0 -1 tan dx Hint: 1+x?

A: As per our guidelines, we are supposed to solve only one question.  Kindly post other questions  as…

Q: 00 Determine whether the improper integral ²+37+1 e dx converges or diverges. Show all your steps.

A: Since there is infinity in the upper bound, this is improper integral of type 1.   To evaluate an…

Q: The improper integral de x+4x+8 converges to converges to * converges to O None diverges

A: Put (X+2) = t and expand

Q: The improper integral 2 dx (x-1)* X - a) Converges to -2 b) Converges to -5 c) Converges to 0 d)…

A: solve the following

Q: The improper integral 1 dx is (x+2)® -1 converges to 5 converges to Diverges 5 converges to 6 None…

A:

Q: x° e* dx 00

A: Given : ∫-∞0x5exdx

Q: 4. Indicate if each improper integral converges or diverges. a) ['te*dt dx c) Lo1+x -2t а) b) x -1…

A: The given integrals are: a) te-2t limit from 0 to infinity.  b) x/(x2-1) limit from 3 to infinity.…

Q: 1 The improper integral -dx x²+2x+5 O None O diverges converges to 3n converges to converges to

A: Solution:To find the integral ∫1∞1x2+2x+5dxFormula:∫1x2+a2dx=1atan-1xa+C

Q: 1. Determine if the integral converges or diverges: re2" dx.

A:

Q: 2. Evaluate the following improper integral if exists (converges). •2 1 dx (x – 2)3/5

A:

Q: dx 3) L. Vx+1

A: Given:

Q: 6. The improper integral 1 dx converges to Vx-5 4 2 попе 1

A:

Q: 5. Use the comparison test to determine if each integral converges or diverges b) 2 2/3-4 a) e-x² dx

A: Solution: 5.a ∫1∞e-x2dx

Q: The improper integral dx 2 x2+4x+8 converges to 4 O None converges to 37 converges to O diverges

A: Topic- integration

Q: (b) Check the convergence of the improper integral dx. I+2

A: Improper integral

Q: Use the previous item to determine if the improper integr 2x – x3 | dx (х — 1)2(г2 + 1) converges or…

A: Given that ∫-∞02x-x3x-12x2+1dxSolution…

Q: (b) Prove that the improper integral ]] 8888 converges. dr dy (1 + x² + y2)3/2

A: Solution: Given improper integral, ∫-∞∞∫-∞∞dxdy1+x2+y232 As we know the convergence of the series is…

Q: Show that for every 0 < p < 1 the integral 1 1 sin – dx xP is both improper and convergent.

A: Answer

Q: In(x84 dx The integral converges to 0 converges to -336 goes to co дoes to -oo converges to 336

A:

Q: 3. Show that for p> 1 and r E (0, 1), the integral below converge: dt tp

A: by limit convergence test we cab prove this, we have to treat the definite integral as summation…

Q: The improper integral dx x²+4x+8 converges to 4 converges to - TC O diverges O None converges to 37

A:

Q: Consider the following improper integral: eV2r dx 00 It can be guaranteed that the integral a)…

A:

Q: Show that for every 0 < p < 1 the integral 1 1 sin = dx xP is both improper and convergent.

A:

Q: 2. Determine the convergence of the improper integral e² In x dx.

A: Take the integral, ∫0∞xlnx=lnxx22-∫0∞1x.x22dx=x2lnx2-x240∞=∞ As after taking x→∞ the limit of the…

Q: How do I do this one?

A: Given integral is The integral is improper and can be evaluated as follows

Q: 11. Determine the divergence or convergence of the following improper integrals and evaluate if it…

A:

Q: Determine if the improper integral (1 e" )2 dx converges or diverges. If it converges, find its…

A:

Q: Determine whether the improper integral -z²+3x+1dx converges or diverges. Show all your steps. e

A:

Q: In x Determine whether the improper integral dx converges or diverges. If it converges, find its…

A: To find the following problem

Q: Determine all values of p for which the improper integral converges.

A: SOLUTION:-    Determine all values of p for which the improper integral converges.   I=∫011xpdx

Q: The improper integral | 1 (x+2)6 dx is converges to 5 3 converges to 5 Diverges O None converges to…

A: We have to solve

Q: -5 1 10) Determine whether the improper integral diverges or converges: ī dx Vx-1

A:

Q: 6. Determine whether the following integral converges or diverges. dr VI!/3 + x

A: First we have to understand following concepts and tests to show convergence and divergence of given…

Q: 1 Determine the convergence of the integral | dx. (2 – x)

A:

Q: The improper integral dx is (x+2)8 1 O None converges to Diverges 5 converges to converges to 5…

A:

Q: 8. 1 The improper integral xp: V(x – 4)³ 4 Converges to -1 Converges to -4 Converges to 1 Diverges

A: To find the improper Integral  Take (x-4) = t And the limits accordingly Then integrate and put the…

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

A: Comparison test :  Suppose for x&gt;a  . If converges then also converges . If diverges then…

Q: The improper integral | 1 x²+2x+5 1 O None O diverges converges to 8 converges to 37 4 O converges…

A:

Q: 10. Determine whether the improper integral J. e cos x dx converges or diverges. If it converges,…

A: Given function :∫0∞e-xcosx dx Rewriting it as limt→∞∫0te-xcosx dx

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.