Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > For a bounded function, is the integral of th...
Start Learning for Free
For a bounded function, is the integral of the function from -infinity to +infinity defined and finite?
- a)Yes
- b)Never
- c)Not always
- d)None of the mentioned
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
For a bounded function, is the integral of the function from -infinity...
If the bounded function, is say y = 2, then the integral ceases to hold. Similarly, if it is just the block square function, it is finite. Hence, it depends upon the spread of the signal on either side. If the spread is finite, the integral will be finite.
Most Upvoted Answer
For a bounded function, is the integral of the function from -infinity...
The correct answer is option 'C' - Not always.
Explanation:
A bounded function is a function that has a finite range. In other words, the function does not take on values that go to infinity or negative infinity.
When we talk about the integral of a bounded function from -infinity to infinity, we are referring to the improper integral. The improper integral is defined as the limit of the definite integral as the limits of integration approach infinity and negative infinity.
In some cases, the integral of a bounded function from -infinity to infinity may be defined and finite. This occurs when the function has a well-behaved behavior as the limits of integration go to infinity and negative infinity.
However, there are cases when the integral of a bounded function from -infinity to infinity is not defined or is infinite. This happens when the function has oscillations, or when it approaches infinity or negative infinity as the limits of integration are reached.
For example, consider the function f(x) = sin(x) / x. This function is bounded because the range of sin(x) is between -1 and 1, and dividing by x does not change the boundedness. However, the integral of this function from -infinity to infinity is not defined because it oscillates and does not converge to a finite value.
Therefore, the integral of a bounded function from -infinity to infinity is not always defined and finite. It depends on the behavior of the function as the limits of integration approach infinity and negative infinity.
Explanation:
A bounded function is a function that has a finite range. In other words, the function does not take on values that go to infinity or negative infinity.
When we talk about the integral of a bounded function from -infinity to infinity, we are referring to the improper integral. The improper integral is defined as the limit of the definite integral as the limits of integration approach infinity and negative infinity.
In some cases, the integral of a bounded function from -infinity to infinity may be defined and finite. This occurs when the function has a well-behaved behavior as the limits of integration go to infinity and negative infinity.
However, there are cases when the integral of a bounded function from -infinity to infinity is not defined or is infinite. This happens when the function has oscillations, or when it approaches infinity or negative infinity as the limits of integration are reached.
For example, consider the function f(x) = sin(x) / x. This function is bounded because the range of sin(x) is between -1 and 1, and dividing by x does not change the boundedness. However, the integral of this function from -infinity to infinity is not defined because it oscillates and does not converge to a finite value.
Therefore, the integral of a bounded function from -infinity to infinity is not always defined and finite. It depends on the behavior of the function as the limits of integration approach infinity and negative infinity.
Attention Electrical Engineering (EE) Students!
To make sure you are not studying endlessly, EduRev has designed Electrical Engineering (EE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Electrical Engineering (EE).
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Top Courses for Electrical Engineering (EE)View all
For a bounded function, is the integral of the function from -infinity to +infinity defined and finite?a)Yesb)Neverc)Not alwaysd)None of the mentionedCorrect answer is option 'C'. Can you explain this answer?
Question Description
For a bounded function, is the integral of the function from -infinity to +infinity defined and finite?a)Yesb)Neverc)Not alwaysd)None of the mentionedCorrect answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about For a bounded function, is the integral of the function from -infinity to +infinity defined and finite?a)Yesb)Neverc)Not alwaysd)None of the mentionedCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a bounded function, is the integral of the function from -infinity to +infinity defined and finite?a)Yesb)Neverc)Not alwaysd)None of the mentionedCorrect answer is option 'C'. Can you explain this answer?.
For a bounded function, is the integral of the function from -infinity to +infinity defined and finite?a)Yesb)Neverc)Not alwaysd)None of the mentionedCorrect answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about For a bounded function, is the integral of the function from -infinity to +infinity defined and finite?a)Yesb)Neverc)Not alwaysd)None of the mentionedCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a bounded function, is the integral of the function from -infinity to +infinity defined and finite?a)Yesb)Neverc)Not alwaysd)None of the mentionedCorrect answer is option 'C'. Can you explain this answer?.
Solutions for For a bounded function, is the integral of the function from -infinity to +infinity defined and finite?a)Yesb)Neverc)Not alwaysd)None of the mentionedCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
Download more important topics, notes, lectures and mock test series for Electrical Engineering (EE) Exam by signing up for free.
Here you can find the meaning of For a bounded function, is the integral of the function from -infinity to +infinity defined and finite?a)Yesb)Neverc)Not alwaysd)None of the mentionedCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
For a bounded function, is the integral of the function from -infinity to +infinity defined and finite?a)Yesb)Neverc)Not alwaysd)None of the mentionedCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for For a bounded function, is the integral of the function from -infinity to +infinity defined and finite?a)Yesb)Neverc)Not alwaysd)None of the mentionedCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of For a bounded function, is the integral of the function from -infinity to +infinity defined and finite?a)Yesb)Neverc)Not alwaysd)None of the mentionedCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice For a bounded function, is the integral of the function from -infinity to +infinity defined and finite?a)Yesb)Neverc)Not alwaysd)None of the mentionedCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
|
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup