Which method can be used to approximate the value of definite integrals?

The Trapezoidal Rule is a numerical method used for approximating the value of definite integrals. This method works by dividing the area under a curve into trapezoids rather than rectangles, which allows for a more accurate estimate of the integral's value. The key idea is to calculate the area of these trapezoids, which is done by averaging the function values at the endpoints of subintervals and multiplying by the width of those intervals.

This approach gives a better approximation than simply using rectangles, especially when the underlying function is not linear. The Trapezoidal Rule is particularly useful when dealing with functions that are difficult to integrate analytically or when an exact integral value is not easily attainable.

In contrast, methods like Newton's Method are primarily used for finding roots of functions rather than evaluating integrals. Vector Addition and Fourier Series, while valuable in their respective contexts, do not serve the purpose of approximating definite integrals in the same direct manner as the Trapezoidal Rule. This makes the Trapezoidal Rule the appropriate choice for this particular question.