9. In evaluating the improper integral dx , which of the following is true? (1-3x)2

Q: ) 「ざs")dx

A:

Q: 1 de is not an improper integral x +1

A:

Q: Evaluate the integral. r 5 (In(x))² x3 dx

A: The integration by parts formula is ∫udv=uv-∫vdu

Q: Evaluate the integral 2 dx where fx) if -2 s xs 0 16-2 if 0xs3

A: Given function is The integral isThe integral can be written as: Plugging the function and applying…

Q: Evaluate the improper integral: e-X dx

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Evaluate the derinite Integral. #5 In(x) dx

A:

Q: Evaluate the improper integral |. 3.x dx or show that it diverges. +1 x?

A:

Q: The improper integral dx x²+4x+8

A: We solve this integration with the help of some basic formula of integration and sone basic…

Q: 3. Evaluate the double integral /sin(x+y) dx dy by using Simpson's 1/3-rule with four sub-intervals.

A: I = ∫0π2∫0π2sin x+ydxdy,

Q: 7. Which of these is a non-elementary integral? In(2y² + 1) А. -dy 4y e-x cosh(2x) В. c. [ e-x +…

A: Non-elementary integral for a given elementary function is an  indefinite integral that is, itself,…

Q: Evaluate the integrals below: 1 2y .dx cos3x а) .dx, b) 0. lelsin3x – 1)

A: Here I am attaching image so that you understand each and every step.

Q: 3. Evaluate the integrals √tanh x sech² xdx

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Q: Evaluate the improper integral or show that it diverges. 9. S- dx 0 (20 - 4x)

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Q: Find a new variable u in integral

A: The integral ∫4x3x4+510dx=∫u10du. We have to find the new variable u.

Q: Compute integral below with the use of substitution. eð 1 -dx x In° x

A:

Q: .1 In x dx ха: -1

A:

Q: So S(x + 3) dy dx 3. Evaluate the double integral:

A:

Q: iSy dx dy 3.

A:

Q: Show using residues that   the integral from 0 to infinity of dx/(1+x^6) equals (2pi)/3

A: We have to show that ∫0∞dx1+x6=2π3 by using residue theorem. Now, ∫Cdz1+z6=∫−RRdx1+x6+∫γdz1+z6 Now,…

Q: 2 Evaluate the improper integral e2a dx, if exists.

A: Evaluate the improper integral  ∫-∞2 e2x dx

Q: 4. Calculate the following integrals: 4 3 dx 1 – x2 dz 25z2 + 1

A:

Q: Evaluate the improper integral A) diverges 3 B 4 с N|9 2 3 -dx

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Q: 4. S dy y³-2y²

A:

Q: 1. Set up the following improper integrals by definition. sin(x) dx 22 — За — 4 а. xe dx с. 4 et b.…

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Q: The improper integral| dx x²+4x+8

A:

Q: 1. Evaluate the improper integral 150 xe dx or state that it diverges.

A:

Q: Evaluate the improper integral : S 4x³e¬9*, dx

A:

Q: Evaluate the improper integral : [° 6x°e¬9æ° dx

A: To solve this question assume 6x^5 = t

Q: Evaluate the improper integral. ∞ ∫dx/((x^2) − 1) 2

A: Given improper Integral

Q: What is the integral that represents the length of the curve from x 2 to x = 4. Select one: 4 ○ ₂²(1…

A: y = x4/4  length of curve formula  = ∫a b1+(dy/dx)2 here limit given from 2 to 4  a = 2  b = 4…

Q: 4. Determine the following integrals 4.2 - dx - a x

A:

Q: Evaluate the improper integral. x In6x dx 0.

A:

Q: - Prove using integrals Proper tos : e even sin()fc) dx=0 -b 9- For even functions.

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Q: Evaluate the double integral dy dx 4. 2.

A:

Q: Evaluate the Cauchy principal value of the given improper integral. 1 [ (x² + 4)² dx

A:

Q: Evaluate the integrals in ∫dx/x

A: Given:               ∫1x dx Let: y=ln x

Q: Compute the given improper integral. Enter the exact value of the answ 13 1 dx x² – 25

A: Here we have to find the exact value of ∫5131x2-25dx=?

Q: determine Ahe impraper integral dx (H+1)(x²+1)

A: ................(1) use the partial fraction  ................(2) ................(3) take x=-1…

Q: 2. Evaluate the improper integral S₂ (5. dx (5-x)4/3 or state that it diverges.

A: The given integral,      ∫28dx5-x43

Q: Evaluate the integral. dy y4 – 16

A:

Q: Evaluate the integrals in ∫dx/1 + ex

A:

Q: Q2: Evaluate the integral fx In x dx using by parts formula

A: Note:- As per our guidelines, We can answer the first question since the exact one wasn’t specified.…

Q: Evaluate the improper integral s dx -2 (2+1)4/3

A: Given: To evaluate ∫-201(x+1)43dx

Q: 2 Which of the following integrals is equal to (3x – 5) dx if u =3x – 7?

A: Given∫123x-5dx

Q: 9 In evaluating the improper integral , (1- 3x)2 dx ,which of the following is true? 3 A lim 3x B…

A: Given,

Q: Calculate the integral approximation S6 for 2 2-a" dx. 1 S6

A:

Q: 2 Evaluate the improper integral e4z dx, if exists. a) The nature of the integral is:

A: Explanation of the solution is given below...

Q: Evaluate the iterated integral. In 5 In 2 4x +4y dy dx 0 1 In 5 In 2 4x+ 4y dy dx = *Ydy dx = 0 1

A: Let's find.

Q: find | (In(x)dx 2 3 Improper Integral

A:

Q: 7) Evaluate the integral Ver+9 dy

A: #7 as per demand Solve integration with help u substitution

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.