Using integral test, what is the value obtained by integrating f(x)? 00 Σ ne n? n=1

Q: Romberg integration for approximating f(x) dx gives R21 = 2 and R22 = 3 then f (0) = O 5/2 O 14 O 17

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Q: ng Properties of Definite Integrals. 2 .2 en f(x) dx = 0 and f(x) dx = 4

A: we know that ∫jkfxdx=∫jlfxdx+∫lkfxdx therefore  ∫-22fxdx=∫-20fxdx+∫02fxdx substitute the values…

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Q: Using integration by parts and taking a > 0, the integral x In(ax)dx is equal to: In a 2 In(2a) - 3…

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Q: 4. | (3t + t) sin(2t) dt

A: Solution: Consider the given integral ; I = ∫3t+t2sin2tdtI = ∫3t sin (2t)dt + ∫t2 sin (2t) dt…

Q: When approximating f(x)dx using Romberg integration, R44 gives an approximation of order: O(h10)…

A: While approximating R(n,n) gives approximation of order (2n+2)

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Q: Comparison Test Determine whether the following integrals converge or diverge.

A: Determine whether the following integrals converge or diverge.

Q: .Using 1 - node Gaussian integration, we have f f(x) dx wif(x₁). What is the value of x₁ ? b-a (c)…

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Q: Using Properties of Definite Integrals. f(x) dx = 0 and | f(2) Given dx = 4 -2 evaluate (a) -2 (b)…

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Q: .Using 1 – node Gaussian integration, we have ſ ƒ(x) dx ≈ w₁ƒ (x₁). What is the value of x₁ ? b+a…

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A: According to Simpson’s rule for integration, ∫abf(x) dx=Δx3f(x0)+4f(x1)+2f(x2) ⋯+4f(xn−1)+f(xn)…

Q: Question: * Using integration by parts, integrate S In 5x dx A. xln 5x – x+ c с. 5xInx - х+ с в. х?…

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Q: Romberg Integration hi h I, I₁ = 1₂ + 1/₂ (1₂-1₁) få ra² dr

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Q: Integration review Evaluate the following integrals.

A: To evaluate the integral: ∫x3+2x2+5x+3x2+x+2dx. Simplifying the integrand. x2+x+2x+1x3+2x2+5x+3x3 +…

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Q: Improper integrals Evaluate the following integrals or state that they diverge.

A: Consider the following integral: I=∫1x-323dx Substitute x-3=t→dx=dt in I:…

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Q: Romberg integration for approximating , f(x) dx gives R21 = 2 and R3 = 3 then f(0): O 5/2 O 14 О 17…

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Q: Improper integrals Evaluate the following integrals or state that they diverge.

A: We have,  fx=lnx The above function is continuous over (0,1] and is discontinuous at zero.

Q: Using integral test, what is the value obtained by integrating f(x)? 1 n In(n) n=2

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