In Simpson’s 1/3 rule, we divide the interval of integration [a, b] into an ………………………number of sub-intervals.

• A) Prime
• B) Odd
• C) Even
• D) None of the given choices

Which of the following is the Global Error for Simpson’s 3/8 Rule while integrating
‘f(x) = Cosx’ in the interval of [0,pi] of equally spaced subinterval of width ‘h =pi/6’ and intermediate point x = pi/2?

• A) -pi/80
• B) 1
• C) pi/80
• D) 0

$$For\,the\,given\,data\,{\text{points}}\,(4,1.3),\,(8,1.5),\,and\,(12,1.9)\,\,the\,divide\,difference\,table\,will\,be\,given\,as$$

• A) $$\begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 4&{1.3}&{0.0062}&{} \\\ 8&{1.5}&{0.1}&{0.05} \\\ {12}&{1.9}&{}&{} \end{array}$$
• B) $$\begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 4&{1.3}&{0.05}&{} \\\ 8&{1.5}&{0.1}&{0.0062} \\\ {12}&{1.9}&{}&{} \end{array}$$
• C) $$\begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 4&{1.3}&{0.1}&{} \\\ 8&{1.5}&{0.35}&{0.0062} \\\ {12}&{1.9}&{}&{} \end{array}$$
• D) $$\begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 4&{1.3}&{0.1}&{} \\\ 8&{1.5}&{0.0062}&{0.05} \\\ {12}&{1.9}&{}&{} \end{array}$$

$$\begin{gathered} For\,the\,given\,divide\,difference\,table \hfill \\ \begin{array}{*{20}{c}} x&y&{1stD.D}&{2ndD.D} \\\ 1&{2.2}&{0.4333}&{} \\\ 4&{3.5}&{0.2}&{ - 0.0389} \\\ 7&{4.1}&{}&{} \end{array} \hfill \\ the\,Newton's\,divide\,difference\,\,{\text{interpolation}}\,formula\,will\,be \hfill \\\ \end{gathered}$$

• A) $$y = f(x) = - 0.0389 + (x - 1)(0.4333) + (x - 1)((x - 4)(2.2)$$
• B) $$y = f(x) = 2.2 + (x - 1)(0.4333) + (x - 1)((x - 4)( - 0.0389)$$
• C) $$y = f(x) = - 0.0389 + (x - 1)(2.2) + (x - 1)((x - 4)(0.4333)$$
• D) $$y = f(x) = 2.2 + (x - 1)( - 0.0389) + (x - 1)((x - 4)(0.4333)$$

In Simpson’s 3/8 rule, we divide the interval of integration into n sub-intervals.
Where n is divisible by.....

• A) 3
• B) None of the given choices
• C) 4
• D) 2

$$\Delta = - - -$$

• A) None
• B) $$\frac{{E - 1}}{2}$$
• C) $E\,\, - \,\,1$
• D) $1 - E$

Given the following data x:1 2 7 11 y:6 10 13 37 Which formula is useful in finding the interpolating polynomial?

• A) None
• B) Newton’s backward difference interpolation formula
• C) Lagrange’s interpolation formula
• D) Newton’s forward difference interpolation formula

If the area under ‘f(x) = x’ in interval [0,2] is subdivided into two equal sub-intervals of width ‘1’ with right end points, then which of the following will be the Truncation Error provided that I(definite integral) = 2 and approximate sum = 3 ?

• A) 0
• B) 2
• C) 1
• D) -1

In Simpson’s 1/3 rule, the global error is of ………………

• A) O(h2)
• B) None of the given choices
• C) O(h4)
• D) O(h3)

Simpson’s 3/8 rule represents the area between the curve y = f(x) in the interval say [a,b] above x-axis by approximating the given curve by the ----------.

• A) Cubic curve through one point
• B) Cubic curve through four points
• C) Cubic curve through three points
• D) Cubic curve through two points

Richardson extrapolation method is used to improve the rate of convergence of a …………

• A) Series
• B) Sequence
• C)
• D)

Richardson extrapolation is method also known as …………

• A) Series acceleration method
• B) Sequence acceleration method
• C)
• D)

$\delta \,\, = \,\, - - - -$

• A) ${E^{\frac{1}{2}}}\,\, + \,\,\,{E^{ - \,\,\,\,\frac{1}{2}}}$
• B) $${E^{\frac{1}{2}}}\,\, - \,\,{E^{ - \,\,\,\,\frac{1}{2}}}$$
• C) $\frac{{{E^{\frac{1}{2}}}\,\, + \,\,\,{E^{ - \,\,\,\,\frac{1}{2}}}}}{2}$
• D) None

Zero-th order divided difference is defined as

• A) y[x0]=x0
• B) y[x0]=y1
• C) y[x0]=y0
• D) None of the given choices

In Composite Trapezoidal formula for integrating a Tabular function, we can approximate it with a polynomial whose ---------- order derivative vanishes.

• A) First
• B) Third
• C) Fourth
• D) Second

The step size “h” in numerical integration over the interval [a,b] is defined as

• A) h=(b/a)/n
• B) h=(a-b)/n
• C) h=(b+a)/n
• D) h=(b-a)/n

Geometrically the definite integral of any continuous function f(x) in the interval [a,b] gives ----------.

• A) Volume with dimensions f(x), ‘a’ and ‘b’
• B) Length of segment AB on real line
• C) Area of Trapezoid with dimension of ‘a’ and ‘b’
• D) Area under f(x) on [a,b]

: What will be the value of first order divided difference f[1,5]for the following data x:0 1 5 y:2 1 5

• A) 3
• B) 1
• C) 0
• D) 2

Which of the following method is simplest one to integrate numerically a given tabular function but give more error?

• A) Trapezoidal method
• B) Simpson’s 3/8 Rule
• C) Simpson’s 1/3 Rule
• D) Rectangular method

The double definite integral of a function is called…………

• A) None of the given choices
• B) Length of the curve
• C) Area under the curve
• D) Volume under the curve