Approximating an integral as an area

Definition

Approximating an integral as an area involves dividing a region into smaller rectangles and summing up their areas to estimate the total area under a curve. It is a method used to find the value of definite integrals when exact calculations are not possible.

Related terms

Riemann Sums: Riemann sums are specific methods for approximating integrals by dividing the region into rectangles and using different rules (such as left endpoint, right endpoint, or midpoint) to determine the height of each rectangle.

Fundamental Theorem of Calculus:

The Fundamental Theorem of Calculus establishes a connection between differentiation and integration. It states that if F(x) is an antiderivative of f(x), then ∫[a,b] f(x) dx = F(b) - F(a), where [a,b] represents the interval over which we are integrating.

Definite Integral:

A definite integral represents the signed area between a function and the x-axis over a given interval [a,b]. It gives us the exact value of the accumulated change in quantity or displacement over that interval.