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--- leibniz_integral_rule [2023/08/12 04:40] – created raju
+++ leibniz_integral_rule [2023/08/12 05:30] (current) – [What is Leibniz integral rule?] raju
@@ Line 1: / Line 1: @@
 ===== Leibniz integral rule =====
 ==== What is Leibniz integral rule? ====
-$$ \frac{d}{dx} \left(\int_{a(x)}^{b(x)} f(x, t) \,dt\right) = f(x, b(x)) \, b^\prime(x) - f(x, a(x)) \, a^\prime(x) + \displaystyle\int_{a(x)}^{b(x)} f_x(x, t) \,dt $$
+$$ \frac{d}{dx} \left(\int_{a(x)}^{b(x)} f(x, t) \,dt\right) = f(x, b(x)) \, b^\prime(x) - f(x, a(x)) \, a^\prime(x) + \int_{a(x)}^{b(x)} \frac{\partial}{\partial x} f(x, t) \,dt $$
 For details, see https://en.wikipedia.org/wiki/Leibniz_integral_rule
+tags | differentiate under the integral sign