Kindly answer completely by applying the concept of improper integrals. Skip if not sure and not willing to answer completely. Thank you! Determine if the improper integral converges or diverges:dx(x2 – 1)4/3IMPROPER INTEGRALS:• If f(x) is continuous on [a, +∞), then the improper integral of f over[a, +o) is defined asf(x) dx = _lim f(x) dx.t-+ Ja• If f(x) is continuous on (-∞, b], then the improper integral of f over(-0, b] is defined as| f(x) dx = _lim f(x) dx.t→-∞JtThe above equalities hold provided the limits exist.In which case, the improper integrals are said to be convergent.If the limit does not exist, the corresponding integral is said to be divergent.

To find: The integral ∫1∞ xx2-143dx. Concept used: ∫a∞ f(x)dx=limt→∞∫at f(x)dx

Answered: Determine if the improper integral…

Math

Calculus

Determine if the improper integral converges or diverges: dx (x² – 1)4/3 1

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Kindly answer completely by applying the concept of improper integrals. Skip if not sure and not willing to answer completely. Thank you!

Determine if the improper integral converges or diverges:
dx
(x2 – 1)4/3
IMPROPER INTEGRALS:
• If f(x) is continuous on [a, +∞), then the improper integral of f over
[a, +o) is defined as
f(x) dx = _lim f(x) dx.
t-+ Ja
• If f(x) is continuous on (-∞, b], then the improper integral of f over
(-0, b] is defined as
| f(x) dx = _lim f(x) dx.
t→-∞Jt
The above equalities hold provided the limits exist.
In which case, the improper integrals are said to be convergent.
If the limit does not exist, the corresponding integral is said to be divergent.

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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