Discussion
A curve passing through the points as given in the table :
| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| y(x) | 0.2 | 0.7 | 1 | 1.3 | 1.5 | 1.7 | 1.9 | 2.1 | 2.3 |
the area bounded by the curve, the \(x\)-axis, \(x = 1\) and \(x = 9\) is :
Answer: A
The area is 11.5 sq. unit.
The table gives 9 equally spaced ordinates with \(h = 1\), that is 8 intervals, an even number, so Simpson's one-third rule applies:
\[ \begin{aligned} A &= \tfrac{h}{3}[(y_{1} + y_{9}) + 4(y_{2} + y_{4} + y_{6} + y_{8}) \\ &\quad + 2(y_{3} + y_{5} + y_{7})] \\ &= \tfrac{1}{3}[2.5 + 4(5.8) + 2(4.4)] \\ &= \tfrac{1}{3}(34.5) = 11.5 \end{aligned} \]
The trapezoidal rule gives \(1.25 + 10.2 = 11.45\), which also rounds to 11.5, so either standard rule leads to option A. 12.0, 10.5 and 10.2 are not produced by any rule; 10.2 is just the sum of the interior ordinates.
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