Definite integrals are the extension after indefinite integrals, definite integrals have limits [a, b]. It gives the area of a curve bounded between given limits.
, It denotes the area of curve F(x) bounded between a and b, where a is the lower limit and b is the upper limit.
Note: If f is a continuous function defined on the closed interval [a, b] and F be an anti derivative of f. Then ![\int_{a}^{b}f(x)dx= \left [ F(x) \right ]_{a}^{b}\right = F(b)-F(a)](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-0f5dfd502d432e802b7950796081d0cc_l3.png "Rendered by QuickLaTeX.com")
Here, the function f needs to be well defined and continuous in [a, b].
Example: 
Solution:
![Since, \int x^{2}=\frac{x^{3}}{3} \newline \newline \textup{Then F(x)} =\frac{x^{3}}{3} \newline \newline [F(x)]_{1}^{4}= F(4)-F(1) \newline \newline =[\frac{4^{3}}{3} - \frac{1^{3}}{3}]=\frac{65}{3}](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-3627c9c053789eee6e71b9eb63beebc9_l3.png "Rendered by QuickLaTeX.com")
Properties of definite integrals –
These properties can be used directly to find the value of particular definite integral and also interchange to other forms if required.
- Related Gate Questions:
- Gate 2014
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