संख्यात्मक समाकलन के लिए सिम्पसन का \(\rm \frac 3 8th\) नियम निम्न में से कौन सा सूत्र है?

This question was previously asked in
Official Sr. Teacher Gr II NON-TSP MATHEMATICS (Held on :29 Oct 2018)
View all RPSC 2nd Grade Papers >
  1. \(\rm \int^{x_n}_{x_0} ydx = \frac {3h}{8} (y_0 + y_n) + 3(y_1 + y_2 + y_4 + y_5 + y_7 + ...+y_{n-1}) + y_n\)
  2. \(\rm \int^{x_n}_{x_0} ydx = \frac {3h}{8} \{(y_0 + y_n) + 3(y_1 + y_2 + y_4 + y_5 + ...+y_{n-1}) + 2(y_3 + y_6 + ...+y_{n-2})\}\)
  3. \(\rm \mathop \smallint \nolimits_{{x_0}}^{{x_n}} ydx = \frac{{3h}}{8}\left\{ {\left( {\frac{{{y_0} + {y_n}}}{2}} \right) + 3\left( {{y_1} + {y_2} + \ldots + {y_{n - 1}}} \right) + 2\left( {{y_3} + {y_6} + \ldots {y_{n - 3}}} \right)} \right\}\)
  4. \(\rm \mathop \smallint \nolimits_{{x_0}}^{{x_n}} ydx = \frac{{3h}}{8}\left\{ {\left( {\frac{{{y_0} + {y_n}}}{2}} \right) + 3\left( {{y_1} + {y_2} + \ldots + {y_{n - 2}}} \right) + 2\left( {{y_3} + {y_6} + \ldots {y_{n - 3}}} \right)} \right\}\)

Answer (Detailed Solution Below)

Option 2 : \(\rm \int^{x_n}_{x_0} ydx = \frac {3h}{8} \{(y_0 + y_n) + 3(y_1 + y_2 + y_4 + y_5 + ...+y_{n-1}) + 2(y_3 + y_6 + ...+y_{n-2})\}\)
Free
Sr. Teacher Gr II NON-TSP GK Previous Year Official questions Quiz 4
8.5 K Users
5 Questions 10 Marks 5 Mins

Detailed Solution

Download Solution PDF

संकल्पना:

संख्यात्मक समाकलन के लिए सिम्पसन का \(\rm \frac 3 8th\) नियम है

\(\rm \int^{x_n}_{x_0} ydx = \frac {3h}{8} \{(y_0 + y_n) + 3(y_1 + y_2 + y_4 + y_5 + ...+y_{n-1}) + 2(y_3 + y_6 + ...+y_{n-2})\}\)

 

इस नियम को न्यूटन के 3/8 नियम के रूप में भी जाना जाता है।

Latest RPSC 2nd Grade Updates

Last updated on Jul 17, 2025

-> RPSC 2nd Grade Senior Teacher Exam 2025 Notification has been released on 17th July 2025 

-> 6500 vacancies for the post of RPSC Senior Teacher 2nd Grade has been announced.

-> RPSC 2nd Grade Senior Teacher Exam 2025 applications can be submitted online between 19th August and 17th September 2025

-> The Exam dates are yet to be announced.

More Solutions of Integral Equations Questions

More Numerical Methods Questions

Get Free Access Now
Hot Links: teen patti download teen patti download apk yono teen patti