Discussion
For an even function \( f \), the integral \( \displaystyle\int_{-a}^{a} f(x)\,dx \) equals
Answer: B
An even function satisfies \( f(-x) = f(x) \), so the graph is a mirror image about the vertical axis and the two halves of the interval contribute equally:
\[ \int_{-a}^{a} f(x)\,dx \;=\; 2\int_{0}^{a} f(x)\,dx. \]
Vanishing is the odd case, and shifting the range to \( [0, 2a] \) samples different values of the function altogether
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