Differentiation assigns to each function a unique derivative by definition. The inverse process seeks to determine whether, for a given function f ( x

To introduce the concept of the definite integral, consider a function f ( x ) defined on a closed interval [ a , b ].

The Fundamental Theorem of Calculus establishes the exact relationship between differentiation and integration. These two operations arise from different initial motivations.

Integration by substitution is a technique used to simplify an integral by introducing a suitable substitution.

Building on the concept of definite integrals, which measure the area between a curve and the x-axis, we can extend the same idea to find the area enclosed between two curves. Let f (

An exponential function is a function of the form e^{x} or \alpha^{x} (with \alpha > 0 and \alpha \neq 1).

In the section on functions, you’ll find the integrals of the main trigonometric functions (for example sine, cosine, tangent, cotangent, and the others.

Trigonometric substitution is a method for evaluating integrals that contain square roots of quadratic expressions.

Improper integrals are integrals in which either the interval of integration is unbounded, or the integrand becomes unbounded at one or more points, or both.

The Riemann integral is built to measure the net area under a bounded function on a closed interval by approximating it with rectangles.