Discussion
The integral \( \displaystyle\int_{1}^{\infty} \frac{dx}{x^{2}} \) is
Answer: C
Evaluate to a finite upper limit and then let it grow:
\[ \int_{1}^{t} \frac{dx}{x^{2}} \;=\; \left[-\frac{1}{x}\right]_{1}^{t} \;=\; 1 - \frac{1}{t} \;\longrightarrow\; 1 \quad (t \to \infty). \]
The tail dies fast enough for the total area to be finite, whereas the same integral with \( 1/x \) in place of \( 1/x^{2} \) diverges logarithmically
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development