Integration can be used to find areas, volumes, central points and many useful things. It is often used to find the area underneath the graph of a function and the x-axis.

Definite Integrals Rules Definite Integral Boundaries ∫abf (x) dx = F (b) − F (a) = limx → b − (F (x)) − limx → a + (F (x)) Odd function If f (x) = −f (−x) ⇒∫−aa f (x) dx = 0

Here are the basic integration rules where each of them can be cross verified by differentiating the result. If you want to see how each of these rules are derived, click on the respective links.

1. Common Integrals. 2. Integrals of Rational Functions. 4. Integrals of Logarithmic Functions. 2 ! i ⋅ i ! 5. Integrals of Trig. Functions.

Jul 23, 2025 · In the following sections, we will explore the most commonly used integration rules that form the foundation of integral calculus. These rules not only simplify the process but also …

Calculus’ basic theorem relates integrals with derivatives, making integral evaluation easier. The power rule, substitution rule, and integration by parts are all important formulae. …

A Review: The basic integration formulas summarise the forms of indefinite integrals for may of the functions we have studied so far, and the substitution method helps us use the table below …

Oct 28, 2025 · The key is to remember that integration is the reverse of differentiation. Start with the basic rules, practice substitution and parts, and soon even difficult problems will feel simple.

The following diagrams show some examples of Integration Rules: Power Rule, Exponential Rule, Constant Multiple, Absolute Value, Sums and Difference. Scroll down the page for more …

A tutorial, with examples and detailed solutions, in using the rules of indefinite integrals in calculus is presented. A set of questions with solutions is also included.