G george gill May 2011 9 0 Jan 3, 2020 #1 Can someone introduce Leibnitz's theorem and show how it is used here. Would be great if one in addition to show how it is used here can add a link to theory about the theorem. I did google it but I got a bit confused. The rest of the theory is here just in case http://people.stern.nyu.edu/wgreene/Lugano2013/Greene-Chapter-14.pdf

Can someone introduce Leibnitz's theorem and show how it is used here. Would be great if one in addition to show how it is used here can add a link to theory about the theorem. I did google it but I got a bit confused. The rest of the theory is here just in case http://people.stern.nyu.edu/wgreene/Lugano2013/Greene-Chapter-14.pdf

romsek Math Team Sep 2015 2,766 1,545 USA Jan 3, 2020 #2 you've seen it just in a less complicated form, sometimes referred to as the fundamental rule of calculus. $\dfrac{\partial}{\partial t}\displaystyle\int_{a(t)}^{b(t)}~f(x)~dx = f(b(t))\dfrac{db}{dt}-f(a(t))\dfrac{da}{dt}$ Reactions: george gill

you've seen it just in a less complicated form, sometimes referred to as the fundamental rule of calculus. $\dfrac{\partial}{\partial t}\displaystyle\int_{a(t)}^{b(t)}~f(x)~dx = f(b(t))\dfrac{db}{dt}-f(a(t))\dfrac{da}{dt}$