Question

The process of evaluating a definite integral from a set of tabulated values of the integrand is called:

• A. Numerical Integration
• B. Extrapolation
• C. Finite Difference
• D. Interpolation

Hint:

Numerical integration is also referred to as "numerical quadrature" in mathematical literature.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
When an integrand $f(x)$ is not known analytically but only as a table of values at discrete points, standard integration cannot be applied.
We use numerical methods to approximate the area under the curve.
Detailed Explanation:
Let us define each term:
- Numerical Integration: This is the process of computing the value of a definite integral $\int_{a}^{b} f(x) dx$ when $f(x)$ is given as a set of tabulated values. Methods include the Trapezoidal Rule, Simpson's Rules, and Weddle's Rule.
- Extrapolation: The process of estimating values outside the range of known data points.
- Finite Difference: A mathematical expression of the form $f(x+h) - f(x)$, used to approximate derivatives.
- Interpolation: The process of estimating values within the range of known data points.

Step 2: Final Answer:
The described process is Numerical Integration, which corresponds to Option (A).