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

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

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Q: (b) dx (1+ x²)² 0,

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

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Q: (b) The improper integral sin x dx converges and is equal to 0.

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Q: 1) Decide whether the given integrals are convergent or divergent. dx b) 1 +x2 - 00

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Q: Define if the given proper integrals converge or diverges a) 4 1 x2 – 2 b)| 1 -dx 7x2 + 1

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

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

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Q: Determine if the improper integral el/x dx x2 converges or diverges. If it converges, find its…

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Q: 1. dx .00 1 1 x 1 2. 1 (3x+1)2 8

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Q: Determine whether the improper integral converges. If so, evaluate it. 6 dx (x-5)3/2 5

A: Here we have,

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

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Q: (1+2x) e¯* dx O Converges O Diverges

A: In the question we have to determine if series converges or diverges.

Q: Use the Comparison Theorem to determine whether the integral is convergent or divergent. arctan(x)…

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Q: Determine whether the improper integral diverges or converges. dx 1. (2x-1)3 7 dx 2. -1* + 1

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Q: Use the comparison theorem to determine whether the integral is convergent or divergent. ∫ ∞ 1…

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Q: Determine, with justification, whether the integral below converges or diverges. dx x15-|sin a|…

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

A: To evaluate the improper integral, split the integral up into two separate integrals at point x=0.…

Q: Determine whether the improper integral diverges or converges. dx 1.co (2x-1)* 00 dx 2. x +1

A: To check weather the given Integral is converges or diverges.

Q: 1. Determine whether the integral given below converges or diverges. dx - x

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

A: Definition used -              Improper integral converges or diverges -               Test of…

Q: Let 0 < a < 1 be a positive real number strictly less than 1. Determine whether the following…

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Q: State whether the following integral converges or diverges: cos x/ √ (2 − sin x) dx  limit: (0 to π/…

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Q: Determine if the integral converges or diverges by comparison.

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Q: Investigate whether the following integral converges sin I

A: We have to investigate whether the given integral ∫0∞sin2xxdx converges or diverges.

Q: At the point of discontinuity on(0, 00), the Fourier Sine integral converges to: OA None f(x+) -…

A: Here  At the point of discontinuity on  0,∞ the Fourier sine integral converges to

Q: Determine whether the integral is convergent or divergent. 0. el/x 5 dx .3 -1

A: The given integral is is convergent , since the function inside the integral is continuous on the…

Q: Show if x, is convergent or divergent T.3 'n sin(x) dx 1+x S'

A: Introduction: The convergence or divergence of an infinite series depends upon the sum of the…

Q: Determine if the following improper integral converges or diverges. If it converges, evaluate xe dx…

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

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

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Q: T/2 2+ sin x dx (iii)

A: The integral converges  see below the calculation and steps

Q: 22. Detemine whether the improper integral converges or diverges, and if it converges, find its…

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Q: Use the Comparison Theorem to determine whether the integral is convergent or divergent.

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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: Determine whether the improper integral or is divergent. ∞ 1 1+2* + e² dx is convergent

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

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Q: Evaluate if the integral converges 1. 1. dx (x-1)7 , sin x dx 3. dx 2.

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Q: Let p > 0. Consider the following improper integrals. 1. Show that dz converges if and only if p <…

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Q: Determine whether the improper integral diverges or converges. dx 1.fº. (2x-1)3

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Q: Determine whether the improper integral or is divergent. S 1 1 1+2* + e²x 2x dx is convergent

A: Given the improper integral as ∫1∞11+2x+e2xdx To determine whether the given series is convergent or…

Q: 0 1 -dx 1 1. 1 dx 1 (3x+1)² 2.

A: Determine whether the following improper integrals are convergent or not.

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

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

A: Write the integrand as exponent of x

Q: Determine if this improper integral will diverge or converge dx (x² – 1)4/3 1 Apply this in solving:…

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

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Q: Evaluate the improper integral if it is convergent. (If it is divergent, type DIVERGENT 7e e-x/2 dx…

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Q: a) Determine if the following integrals are convergent or divergent: sin? (x) x +1 dx dx Vr4 – x -

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Q: 7. Determine whether the given integral is convergent or 1 dx? x*+1 divergent Page of a. convergent…

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