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Leibniz integral rule
Differentiation under the integral sign formula
Leibniz integral rule
In calculus, the Leibniz integral rule or the Leibniz rule for differentiation under the integral sign, named after Gottfried Wilhelm Leibniz, states that for an integral of the form ∫ a ( x ) b ( x ) f ( x , t ) d t , {\displaystyle \int _{a(x)}^{b(x)}f(x,t)\,dt,} where − ∞ < a ( x ) , b ( x ) < ∞ {\displaystyle -\infty <a(x),b(x)<\infty } and the integrands are functions dependent on x , {\displaystyle x,} the derivative of this integral is expressible as...
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