Free Printable ICS numerical integration

1.

In numerical integration the width of the sub intervals is given by

a)

$h=\frac{x_n-x_0}{n}$

b)

$h=\frac{x_n+x_0}{n}$

c)

$h=\frac{x_0-x_n}{n}$

d)

none of thesse

2.

In Trapezoidal rule, for the interval (2,5) if h=0.5 then the value of n is_________

a)

5

b)

2

c)

6

d)

4

3.

Simpson’s 1/3 rule is applicable for five ordinates.

a)

True

b)

False

4.

Simpson’s 3/8 rule is applicable for nine ordinates.

a)

True

b)

False

5.

h=0.25

a)

0.388

b)

0.188

c)

0.288

d)

0.488

6.

Error in SIMPSON'S rule is of order

a)

h

b)

h²

c)

h³

d)

h⁴

7.

Estimate f(1.5) using Lagrange interpolation.

a)

−0.8673

b)

-0.7214

c)

−0.9773

d)

-0.9113

8.

Find f(2) for the data f(0) = 1, f(1) = 3 and f(3) = 55 using Newton's divided difference formula.

a)

25

b)

21

c)

23

d)

32

9.

Find f(0.25) using Newton's divided difference formula

a)

3.826

b)

3.2567

c)

3.2113

d)

3.912

10.

a)

3.125

b)

3.327

c)

3.542

d)

3.837

11.

Given the two points $\left(a,f\left(a\right)\right),\left(b,f\left(b\right)\right)$ , the linear Lagrange polynomial $f1\left(x\right)$ that passes through these two points is given by

a)

$f1\left(x\right)=\frac{x-b}{a-b}f\left(a\right)+\frac{x-a}{a-b}f\left(b\right)$

b)

$f1\left(x\right)=\frac{x}{b-a}f\left(a\right)+\frac{x}{b-a}f\left(b\right)$

c)

$f1\left(x\right)=f\left(a\right)+\frac{f\left(b\right)-f\left(a\right)}{b-a}\left(b-a\right)$

d)

$f1\left(x\right)=\frac{x-b}{a-b}f\left(a\right)+\frac{x-a}{b-a}f\left(b\right)$

12.

Based on the data given, which is the suitable type of polynomial to do the approximation?

a)

Linear

b)

Quadratic

c)

Cubic

d)

Quartic

13.

The methods to find the polynomials approximation are ..

a)

Lagrange interpolation

b)

Newton's Divided Difference

c)

Natural Cubic Spline

d)

Clamped Cubic Spline

ICS numerical integration

Total questions: 13

Worksheet time: 1hrs 5mins

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