Numerical Analysis-Numerical Integration (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 1 - 2 of 2

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Question number: 1

» Numerical Analysis » Numerical Integration

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Evaluate the following by taking seven ordinates of the integrand:

Equation

Explanation

The seven ordinates of the integrand using Simpson’s rule is

Equation

Where h = 1/6 (b-a) and y k =f (a + kh) for k = 0, 1, 2, 3, 4, 5, 6

Here, b = 1, a = 0, h = 1/6, f (x) = Equation

Equation

Equation

Equation

… (10 more words) …

Question number: 2

» Numerical Analysis » Numerical Integration

Appeared in Year: 2012

Essay Question▾

Describe in Detail

The speed y (in km/hr) of a car at different points of time x between 10: 00 a. m. and 10: 40 a. m. on some day was recorded as follows:

Time x (a. m. )

10.00

10.10

10.20

10.30

10.40

Speed y (in km/hr)

24.2

35.0

41.3

42.8

39.2

Calculate the approximate distance covered by the car between 10: 00 a. m. and 10: 40 a. m. on that day using Simpson’s one-third formula for numerical integration.

Explanation

Answer: T he one-third rule of the integrand using Simpson’s rule is

Equation

Here n = 4, b = 10: 40 = 40 minutes, a = 10.00 = 0 minutes, h= (b-a) /n = 10 minutes

The distance covered by the car between 10: 00 a. m. and 10: 40

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