Discussion
The average of function f(x) = sin x in the interval 0 to π is :
Answer: B
The average is \(2/\pi\).
The mean value of a function over an interval is its integral divided by the length of the interval:
\[ \begin{aligned} \bar{f} &= \frac{1}{\pi - 0}\int_{0}^{\pi} \sin x\, dx \\ &= \frac{1}{\pi}\big[-\cos x\big]_{0}^{\pi} \\ &= \frac{1}{\pi}(1 + 1) = \frac{2}{\pi} \end{aligned} \]
That is about 0.64. The value \(1/\pi\) forgets that \(-\cos x\) changes by 2, not 1, and \(4/\pi\) doubles the result. The value 1/2 is the average of \(\sin^{2} x\), the quantity behind RMS values, not of \(\sin x\).
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