Integral Connections

The definite integral, $\int_a^b f(x),dx$, is a number that represents the net signed area between the lines $x=a$, $x=b$, $y=0$, and the curve $y=f(x)$. It is defined as a limit of certain finite sums, called Riemann sums.

The definite integral can be computed as a limit of certain finite sums. These computations are intimately connected with differentiation, as stated by the Fundamental Theorem of Calculus, Part II.

The Fundamental Theorem of Calculus, Part II, tells us that the computations of definite integrals are intimately connected with differentiation.

The computations of definite integrals and differentiation are intimately connected, as stated by the Fundamental Theorem of Calculus, Part II. The theorem tells us that these computations are related in a surprising way, allowing us to compute definite integrals using differentiation techniques.

The indefinite integral is related to the definite integral through the Fundamental Theorem of Calculus, Part II. The indefinite integral is the antiderivative of a function, while the definite integral represents the net signed area between the lines $x=a$, $x=b$, $y=0$, and the curve $y=f(x)$. The Fundamental Theorem of Calculus, Part II, establishes a relationship between these two concepts.