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The value of the improper integral integration 1 tend to infinity 1/x^5 dx is given by A. 1/4. 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^...
Calculation of Improper Integral:
Given integral: ∫1 to ∞ 1/x^5 dx
Break down the integral:
- ∫1 to ∞ 1/x^5 dx = lim(a→∞) ∫1 to a 1/x^5 dx
Integrate the function:
- ∫1 to a 1/x^5 dx = [-1/(4x^4)] from 1 to a
- = [-1/(4a^4)] - [-1/4]
Apply the limit:
- lim(a→∞) [-1/(4a^4)] - [-1/4] = 0 - [-1/4] = 1/4
Therefore, the value of the improper integral ∫1 to ∞ 1/x^5 dx is 1/4. Hence, the correct answer is A. 1/4.
Given integral: ∫1 to ∞ 1/x^5 dx
Break down the integral:
- ∫1 to ∞ 1/x^5 dx = lim(a→∞) ∫1 to a 1/x^5 dx
Integrate the function:
- ∫1 to a 1/x^5 dx = [-1/(4x^4)] from 1 to a
- = [-1/(4a^4)] - [-1/4]
Apply the limit:
- lim(a→∞) [-1/(4a^4)] - [-1/4] = 0 - [-1/4] = 1/4
Therefore, the value of the improper integral ∫1 to ∞ 1/x^5 dx is 1/4. Hence, the correct answer is A. 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. 1/4. 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. 1/4. 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. 1/4. 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. 1/4. 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. 1/4. 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. 1/4. 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. 1/4. B. 1/6. C. 6. D. -5/6.?.
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