UPSC Exam > UPSC Questions > The value of the improper integral integratio...
Start Learning for Free
The value of the improper integral integration 1 tend to infinity 1/x^5 dx is given by A. Infinity. B. 1/6. C. 6. D. -5/6.?
Most Upvoted Answer
The value of the improper integral integration 1 tend to infinity 1/x^...
Understanding the Integral:
The given improper integral is ∫1 to infinity of 1/x^5 dx. This integral represents the area under the curve of the function 1/x^5 from 1 to infinity.
Analysis of the Integral:
To determine the value of this improper integral, we need to find the limit of the integral as the upper limit tends to infinity. Mathematically, we write this as ∫1 to A of 1/x^5 dx as A approaches infinity.
Calculating the Integral:
∫1 to A of 1/x^5 dx = [-1/(4x^4)] from 1 to A
= [-1/(4A^4)] - [-1/(4*1^4)]
= -1/(4A^4) + 1/4
Limit as A approaches Infinity:
As A approaches infinity, the value of -1/(4A^4) approaches 0. Therefore, the value of the integral ∫1 to infinity of 1/x^5 dx is 1/4.
Final Answer:
Therefore, the value of the improper integral ∫1 to infinity of 1/x^5 dx is 1/4.
The given improper integral is ∫1 to infinity of 1/x^5 dx. This integral represents the area under the curve of the function 1/x^5 from 1 to infinity.
Analysis of the Integral:
To determine the value of this improper integral, we need to find the limit of the integral as the upper limit tends to infinity. Mathematically, we write this as ∫1 to A of 1/x^5 dx as A approaches infinity.
Calculating the Integral:
∫1 to A of 1/x^5 dx = [-1/(4x^4)] from 1 to A
= [-1/(4A^4)] - [-1/(4*1^4)]
= -1/(4A^4) + 1/4
Limit as A approaches Infinity:
As A approaches infinity, the value of -1/(4A^4) approaches 0. Therefore, the value of the integral ∫1 to infinity of 1/x^5 dx is 1/4.
Final Answer:
Therefore, the value of the improper integral ∫1 to infinity of 1/x^5 dx is 1/4.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
The value of the improper integral integration 1 tend to infinity 1/x^5 dx is given by A. Infinity. B. 1/6. C. 6. D. -5/6.?
Question Description
The value of the improper integral integration 1 tend to infinity 1/x^5 dx is given by A. Infinity. B. 1/6. C. 6. D. -5/6.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The value of the improper integral integration 1 tend to infinity 1/x^5 dx is given by A. Infinity. B. 1/6. C. 6. D. -5/6.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The value of the improper integral integration 1 tend to infinity 1/x^5 dx is given by A. Infinity. B. 1/6. C. 6. D. -5/6.?.
The value of the improper integral integration 1 tend to infinity 1/x^5 dx is given by A. Infinity. B. 1/6. C. 6. D. -5/6.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The value of the improper integral integration 1 tend to infinity 1/x^5 dx is given by A. Infinity. B. 1/6. C. 6. D. -5/6.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The value of the improper integral integration 1 tend to infinity 1/x^5 dx is given by A. Infinity. B. 1/6. C. 6. D. -5/6.?.
Solutions for The value of the improper integral integration 1 tend to infinity 1/x^5 dx is given by A. Infinity. B. 1/6. C. 6. D. -5/6.? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of The value of the improper integral integration 1 tend to infinity 1/x^5 dx is given by A. Infinity. B. 1/6. C. 6. D. -5/6.? defined & explained in the simplest way possible. Besides giving the explanation of
The value of the improper integral integration 1 tend to infinity 1/x^5 dx is given by A. Infinity. B. 1/6. C. 6. D. -5/6.?, a detailed solution for The value of the improper integral integration 1 tend to infinity 1/x^5 dx is given by A. Infinity. B. 1/6. C. 6. D. -5/6.? has been provided alongside types of The value of the improper integral integration 1 tend to infinity 1/x^5 dx is given by A. Infinity. B. 1/6. C. 6. D. -5/6.? theory, EduRev gives you an
ample number of questions to practice The value of the improper integral integration 1 tend to infinity 1/x^5 dx is given by A. Infinity. B. 1/6. C. 6. D. -5/6.? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
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