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The value of the improper integral integration 1 tend to infinity 1/x^5 dx is given by A. 0. 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^...
Approach:
To find the value of the improper integral, we need to evaluate the limit of the definite integral as the upper limit tends to infinity. In this case, the integral is of the form ∫1 to ∞ 1/x^5 dx.
Calculation:
The integral can be expressed as ∫1 to t 1/x^5 dx, where t approaches infinity.
Integrating the function 1/x^5 with respect to x, we get -1/(4x^4).
Therefore, the integral becomes [-1/(4t^4) - (-1/4)] as t approaches infinity.
This simplifies to 1/4t^4 as t tends to infinity.
Taking the limit of 1/4t^4 as t approaches infinity, we get 0.
Conclusion:
Therefore, the value of the improper integral ∫1 to ∞ 1/x^5 dx is 0. Hence, the correct answer is option A.
To find the value of the improper integral, we need to evaluate the limit of the definite integral as the upper limit tends to infinity. In this case, the integral is of the form ∫1 to ∞ 1/x^5 dx.
Calculation:
The integral can be expressed as ∫1 to t 1/x^5 dx, where t approaches infinity.
Integrating the function 1/x^5 with respect to x, we get -1/(4x^4).
Therefore, the integral becomes [-1/(4t^4) - (-1/4)] as t approaches infinity.
This simplifies to 1/4t^4 as t tends to infinity.
Taking the limit of 1/4t^4 as t approaches infinity, we get 0.
Conclusion:
Therefore, the value of the improper integral ∫1 to ∞ 1/x^5 dx is 0. Hence, the correct answer is option A.
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The value of the improper integral integration 1 tend to infinity 1/x^5 dx is given by A. 0. 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. 0. 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. 0. 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. 0. 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. 0. 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. 0. 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. 0. B. 1/6. C. 6. D. -5/6.?.
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