Properties of Definite Integrals. Properties of Integrals and Evaluating Definite Integrals - Duration: 9:48. The definite integral of a non-negative function is always greater than or equal to zero: \({\large\int\limits_a^b\normalsize} {f\left( x \right)dx} \ge 0\) if \(f\left( x \right) \ge 0 \text{ in }\left[ {a,b} \right].\) The definite integral of a non-positive function is always less than or equal to zero: This applet explores some properties of definite integrals which can be useful in computing the value of an integral. We will be exploring some of the important properties of definite integrals and their proofs in this article to get a better understanding. Properties of Definite Integration . Professor Dave Explains 40,026 views. We have seen that the definite integral, the limit of a Riemann sum, can be interpreted as the area under a curve (i.e., between the curve and the horizontal axis). Integrals in maths are used to find many useful quantities such as areas, volumes, displacement, etc. Integration is the estimation of an integral. Both indefinite and definite integration are interrelated and indefinite integration lays the groundwork for definite integral. Definite integration is an important component of integral calculus which generally fetches a good number of questions in various competitive exams. 9:48.

It is just the opposite process of differentiation.