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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.?
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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.
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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.?
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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.?.
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