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what is newton -leibnitz's rule how to apply it in a question ?explain with 3-4 example
Dear pradyot
Leibniz Integral Rule
The Leibniz integral rule gives a formula for differentiation of a definite integral whose limits are functions of the differential variable,
where the partial derivative of f indicates that inside the integral only the variation of ƒ ( x, α ) with α is considered in taking the derivative.
Here, we consider the integration of
where both , by differentiating under the integral sign.
Let us first find
Dividing both the numerator and the denominator by yields
The limits of integration being independent of gives us
whereas gives us
Equating these two relations then yields
In a similar fashion, pursuing yields
Adding the two results then produces
which is the value of the integral
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