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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