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

- 0
- 0.25
- 0.5
- 1

2. The error in numerically computing the integral $\int_{0}^{\pi}(\sin x+\cos x)dx$ using the trapezoidal rule with three intervals of equal length between 0 and π is

- 0.158
- 0.25
- 0.20
- 0.187

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

- linear
- parabolic
- logarithmic
- 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 $\int_{0}^{0.4}f(x) dx$ is

- 44
- 22
- 11
- 33

5. Using a unit step size, the volume of integral $\int_{1}^{2}(x\ln x)dx$ by trapezoidal rule is

- 0.600
- 0.493
- 0.593
- 0.693

6. The integral $\int_{x_1}^{x_2}(x^2)dx$ with x_{2} > x_{1} > 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?

- J > I
- J < I
- J = I
- insufficient data to determine the relationship

7. Using the trapezoidal rule, and dividing the interval of integration into three equal subintervals, the definite integral $\int_{1}^{2}\left | x \right |dx$ by trapezoidal rule is

- 1.58
- 1.25
- 1.11
- 1.43

8. The definite integral $\int_{1}^{3}(\frac{1}{x})dx$ is evaluated using trapezoidal rule with a step size of 1. The correct answer is

- 1.165
- 1.695
- 1.213
- 1.434

9. The value of $\int_{2.5}^{4}(\ln x)dx$ calculated using the trapezoidal rule with five subintervals is

- 1.2000
- 1.4258
- 1.7533
- 1.6589

10. The minimum number of equal length subintervals needed to approximate $\int_{1}^{2}(xe^x)dx$ to an accuracy of at least (1/3) x 10^{-6} using the trapezoidal rule is

- 1000e
- 1000
- 100e
- 100

11. A calculator has accuracy up to 8 digits after decimal place. The value of $\int_{0}^{2\pi}(\sin x)dx$ when evaluated using this calculator by trapezoidal method with 8 equal intervals, to 5 significant digits is

- 0.00000
- 1.0000
- 0.00500
- 0.00025

12. A 2^{nd} degree polynomial, f(x) has values of 1, 4 and 15 at x = 0, 1 and 2, respectively. The integral $\int_{0}^{2}f(x)dx$ 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?

- -4/3
- -2/3
- 0
- 2/3