5) Prove whether or not the following integrals converge or diverge. a) Si b) S, 1 dt In(t)-1

Q: The value of the binary integral is e-xy dxdy . (where a, b are positive real constants) are

A:

Q: dx Determine if the integral 2 J+x/T converges or diverges.

A: We use substitution method

Q: Determine whether the follOwing improper integral cC 1 dx a In x 00 1 This integral converges to In…

A: Given that: ∫2∞1x.lnxdx

Q: a) Solve the following iterated integrals holding Fubini's Theorem. 1. 1 '(x+y)dydx

A:

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) dt…

A:

Q: The set of all values of p which makes the integral x* dx is divergent is a) (-1, 0) b) (-n,-1) c)…

A:

Q: 4. Evaluate the following integral using three-point Gauss-Legendre quadrature: 3.5 dx Vx2 - 4 3.

A: We will use the three-point Gauss-Legendre quadrature. First we convert the given integral…

Q: Given A B 1 -dx, determine all value/values of P for which the improper integral converges? to…

A: Using p-test form infinite limit we know that:  For a>0: If p>1 then ∫a∞1xpdx converges. Here…

Q: (b) Determine whether the following integrals converge. (i) ² x²+x-1 x5 + 3x dx, /2 5²1² ln(1+x²) x…

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Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A: We need to evaluate the integral using the fundamental theorem of calculus:

Q: In 5 through 6 determine whether the improper integral converges or diverges. If it converges…

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Q: Estimate the integral f, dx using a left-hand Riemann sum and 4 2

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Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A:

Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A: Given: Definite integral Sum Rule of integration,

Q: Consider the improper integral and the propositions dx J = = 6of foo x² + 3 1- The integral J…

A: Find out the correct statement.

Q: 3. Decide if the following improper integrals converge or diverge. dx (a) x2 + 4 (b) xe" dr da (c)…

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Q: Evaluate the integrals in Exercises 1. esin (e) dx 2. e cos (3e – 2) dt

A: Given the integration I=∫exsin(ex)dx

Q: 1 et dx 1 (1 — е*)2

A:

Q: Evaluate |- e*dz where c is |z|=3 using Cauchy's integral formula „(1+2),

A:

Q: Evaluate the integral, if it exists.

A: Given: ∫-π4π4t4 tant2+costdt

Q: Calculate the integral of f(x, y) = 9x over the region D bounded above by y = x(2 – x) and below by…

A: We will evaluate the given integral over the region D.

Q: Evaluate the integral S (t³ In ti+ 3t sin (t*) j+ ) dt. 1-2 x1)

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Q: Evaluate the integral f(Vt,et) dt. t+1'

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Q: 1- Find the integral of: 2 cot - de T/2 A- B- / dr Vr

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Q: The improper integral 2e*dx is: (a)converge to 2 (b) converge to – 2 (c) convergeto 0 (d) diverge a…

A: Solution is given below:

Q: Compute the following integral below using integration by parts. So t³ In(t)dt. •1

A:

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) dt…

A: We need to evaluate the integral using the given substitution

Q: Evaluate the integrals in ∫7cos t sin t dt

A: Given Integral,I=∫7 cos t sin t dt

Q: Evaluate the integrals ∫dt/t√t

A: Consider the given integration as I=∫dttt or I=∫t-32dt As we know, ∫xndx=xn+1n+1

Q: 4) Determine whether the improper integral diverges a) fx'e *dx or converges: 1 b) J (7x +1)³ 1

A:

Q: Given Ve +4 G(x)= [ In(r² -4) dt Ve +4 find G'(x) by using the Fundamental Theorem of Calculus. b)…

A: (a.)   Given :  G(x)=∫ex+4e2x+4ln(t2-4)…

Q: Evaluate the integral f (t* In ti+ 3t° sin (t*) j + ) dt. (x+1) -2

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Q: Assume that the conditions of the fundamental theorem are satisfied for the integral . Vf · dĩ where…

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Q: Express the given integral f, 2x dx as the limit of Riemann sum. a. 2x dx = lim E-(1+) G+1)* E- d.…

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Q: 7. (sin x + cos y) dA, where S is the square 0<x <7/2,0 < y < n/2

A: The solution are next step

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

A: Given problem:-

Q: 5) Prove whether or not the following integrals converge or diverge. b) S; In(t)-1 dt

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Q: Evaluate the following integrals (taken anticlockwise) using Cauchy's theorem: (f) P.„(²+1)² eiz dz…

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Q: If L {f(t); p} = F(p), then ° f(t) S dt = F(u) du, assuming that the integrals converge and hence…

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Q: or show that the integral Integrate the following diverges: Зе In sin x ii) dx COS X 2e

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Q: 3. Determine if the following improper integrals converge, if it does, determine the value of the…

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Q: Evaluate the integral.  integral  t  3sin 2  t dt

A: To evaluate the integral: ∫3sin2tdt. We know that, sin2x=1-cos2x2 Therefore, using this formula,…

Q: se the fact that 1 dr %3D 2e2 Ae 2r +C p either evaluate the improper integral -d.r, or show that it…

A: we have to find integration.

Q: 4. Evaluate the following integral using three-point Gauss-Legendre quadrature: 3.5 dx Vx2 – 4 3.

A:

Q: 22 Calculate the value of the integral over the following C curves, a) C:|2+1| = 1

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

Q: . Evaluate the integral S (t* In ti+ 3t sin (t*) j+ ) dt. +1)

A:

Q: († ++) S(1 + +)*dt

A: Given is: The integral is as:∫t+1t3dt   To find: We need to solve the integral.

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.