While applying Simpson's three eighth rule for numerical... | Agrigyan

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ICAR AIEEA PG Statistical Science 14 July 2023 Shift-1 Paper

MCQ (Single Correct)

While applying Simpson's three eighth rule for numerical integration, the number of sub-intervals should be taken as multiple of :

संख्यात्मक समाकलन के लिए सिम्पसन के तीन-आठवें ($3/8$) नियम को लागू करते समय, उप-अंतरालों की संख्या को किसका गुणज लिया जाना चाहिए?

$2$ $2$ $3$ $3$ $8$ $8$ $6$ $6$

Requirements for Newton-Cotes numerical quadrature formulas:

Trapezoidal Rule: Number of sub-intervals $n$ can be any positive integer (multiple of 1).
Simpson's 1/3 Rule: Based on quadratic interpolation, requires $n$ to be an even number (multiple of 2).
Simpson's 3/8 Rule: Based on cubic polynomials fitting four points (three sub-intervals at a time), requires the total number of sub-intervals $n$ to be a multiple of 3.
Weddle's Rule: Requires $n$ to be a multiple of 6.

Option breakdown:
Multiple of 2 applies to Simpson's 1/3 rule.
Multiple of 3 is the exact condition for Simpson's 3/8 rule.
Multiple of 8 is not a requirement.
Multiple of 6 applies to Weddle's rule.

संख्यात्मक समाकलन नियमों के लिए उप-अंतरालों की आवश्यकताएँ:

समलम्बीय नियम: उप-अंतरालों की संख्या कोई भी पूर्णांक हो सकती है।
सिम्पसन का $1/3$ नियम: परवलयिक अंतर्वेशन पर आधारित, उप-अंतरालों की संख्या सम (2 का गुणज) होनी चाहिए।
सिम्पसन का $3/8$ नियम: त्रिघात बहुपद पर आधारित, तीन-तीन अंतरालों के संयोजन हेतु उप-अंतरालों की संख्या 3 का गुणज होनी चाहिए।
वेडल का नियम: 6 का गुणज होना आवश्यक है।

विकल्पों का विश्लेषण:
का गुणज सिम्पसन $1/3$ नियम के लिए होता है।
का गुणज सिम्पसन $3/8$ नियम की अनिवार्य शर्त है।
8 का गुणज अमान्य है।
6 का गुणज वेडल के नियम के लिए होता है।

Explanation not matching this question? क्या व्याख्या इस प्रश्न से मेल नहीं खा रही? Report

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