# Trapezoidal Rule MCQ

1. P(0,3), Q(0.5,4) and R(1,5) are three points on the curve defined by f(x). Numerical integration is carried out using both trapezoidal rule and simpson’s rule within limits x = 0 and x = 1 for the curve. The difference between the two results will be

1. 0
2. 0.25
3. 0.5
4. 1

2. The error in numerically computing the integral using the trapezoidal rule with three intervals of equal length between 0 and π is

1. 0.158
2. 0.25
3. 0.20
4. 0.187

3. Numerical integration using trapezoidal rule gives the best result for a single variable function, which is

1. linear
2. parabolic
3. logarithmic
4. hyperbolic

4. The values of function f(x) at 5 discrete points are given below:

 x 0 0.1 0.2 0.3 0.4 f(x) 0 10 40 90 160

Using trapezoidal rule step size of 0.1, the value of is

1. 44
2. 22
3. 11
4. 33

5. Using a unit step size, the volume of integral by trapezoidal rule is

1. 0.600
2. 0.493
3. 0.593
4. 0.693

6. The integral with x2 > x1 > 0 is evaluated analytically as well as numerically using a single application of the trapezoidal rule. If I is the exact value of the integral obtained analytically and J is the approximate value obtained using the trapezoidal rule, which of the following statements is correct about their relationship?

1. J > I
2. J < I
3. J = I
4. insufficient data to determine the relationship

7. Using the trapezoidal rule, and dividing the interval of integration into three equal subintervals, the definite integral by trapezoidal rule is

1. 1.58
2. 1.25
3. 1.11
4. 1.43

8. The definite integral is evaluated using trapezoidal rule with a step size of 1. The correct answer is

1. 1.165
2. 1.695
3. 1.213
4. 1.434

9. The value of calculated using the trapezoidal rule with five subintervals is

1. 1.2000
2. 1.4258
3. 1.7533
4. 1.6589

10. The minimum number of equal length subintervals needed to approximate to an accuracy of at least (1/3) x 10-6 using the trapezoidal rule is

1. 1000e
2. 1000
3. 100e
4. 100

11. A calculator has accuracy up to 8 digits after decimal place. The value of when evaluated using this calculator by trapezoidal method with 8 equal intervals, to 5 significant digits is

1. 0.00000
2. 1.0000
3. 0.00500
4. 0.00025

12. A 2nd degree polynomial, f(x) has values of 1, 4 and 15 at x = 0, 1 and 2, respectively. The integral is to be estimated by applying the trapezoidal rule to this data. What is the error (defined as “true value-approximate value”) in the estimate?