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===Definite Integration===

===Definite Integration===

{{main|Definite integral}}

{{main|Definite integral}}

This kind of integral is called a ''definite integral'', written with the limits:

This kind of integral is called a ''definite integral'', written with the limits <math>[a,b]</math>:

:<math>\int_a^b x^2\ \mathrm{d}x = \frac{b^3}{3} - \frac{a^3}{3}\,</math>,

:<math>\int_a^b f(x)\,dx = F(b) - F(a)</math>

The above is a simplified "intuitive" treatment of calculus and of this theorem.  The actual "rigorous" proof, "rigorous" definitions of derivative and integral, and statement of the conditions under which the theorem is true, are beyond the scope of this article.

The above is a simplified "intuitive" treatment of calculus and of this theorem.  The actual "rigorous" proof, "rigorous" definitions of derivative and integral, and statement of the conditions under which the theorem is true, are beyond the scope of this article. Definite integrals are strongly connected to the [[Fundamental Theorem of Calculus]].

== External Links ==

== External Links ==