Improper Integrals
The value of ∫₁^∞ (1/x²) dx is
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About This Question
- Subject
- mathematics
- Chapter
- integral calculus
- Topic
- improper integrals
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
1
- Define Improper Integral: Treat the upper limit as a limit to infinity.
- limb→∞∫1bx−2dx.
- Integrate: Antiderivative is −1/x.
- [−x1]1b=(−b1)−(−11)
- =1−b1.
- Take Limit: As b→∞,b1→0.
- Result =1−0=1.
- Because the limit is finite, we say this improper integral converges to 1.
This hard difficulty mathematics question is from the chapter integral calculus, covering the topic of improper integrals. It appeared in the 2025 exam.
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