# JEE Main & Advanced Mathematics Definite Integrals Integration of Piecewise Continuous Functions

Integration of Piecewise Continuous Functions

Category : JEE Main & Advanced

Any function $f(x)$ which is discontinuous at finite number of points in an interval $[a,\,\,b]$ can be made continuous in sub-intervals by breaking the intervals into these subintervals. If $f(x)$ is discontinuous at points ${{x}_{1}},\,\,{{x}_{2}},\,\,{{x}_{3}}..........{{x}_{n}}$ in $(a,\,\,b)$, then we can define subintervals $(a,{{x}_{1}}),({{x}_{1}},{{x}_{2}}).............({{x}_{n-1}},\,\,{{x}_{n}}),\,({{x}_{n}},b)$ such that $f(x)$ is continuous in each of these subintervals. Such functions are called piecewise continuous functions. For integration of piecewise continuous function, we integrate $f(x)$ in these sub-intervals and finally add all the values.

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