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Improper Integrals: Convergence Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
FAQs on Improper Integrals: Convergence Video Lecture - Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
| 1. What is an improper integral? |  |
Ans. An improper integral is a type of definite integral that has either an infinite limit of integration or an integrand that is not defined at certain points within the interval of integration.
| 2. How do you determine if an improper integral converges? | |
Ans. To determine if an improper integral converges, you need to evaluate the integral over the interval of integration and check if the result is a finite number. If it is, then the integral converges; otherwise, it diverges.
| 3. What is the difference between a convergent and a divergent improper integral? | |
Ans. A convergent improper integral is one that has a finite value when evaluated, meaning the integral exists. On the other hand, a divergent improper integral is one that does not have a finite value when evaluated, indicating that the integral does not exist.
| 4. What are the different types of improper integrals? | |
Ans. There are two types of improper integrals: Type 1, which has infinite limits of integration, and Type 2, which has an integrand that is not defined at certain points within the interval of integration.
| 5. Can an improper integral converge even if it has an unbounded integrand? | |
Ans. Yes, an improper integral can still converge even if it has an unbounded integrand. The convergence of an improper integral depends on the behavior of the integrand as it approaches the points of discontinuity or the infinite limits of integration. If the integral can be evaluated to a finite value despite the unboundedness of the integrand, it converges.
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