Htykuut

up vote 2 down vote favorite Someone the other day told me about the idea of evaluating integrals using horizontal instead of vertical bars (apparently something to do with Lebesque integration but thats way too complicated for me to understand). So I was thinking about this and it occurred to me that and inverse function flips a function that in a way taking its integral is taking the original integral but horizontally. This then lead me to come up with 2 identities I'm not sure are correct and I established graphically. $$ int_0^xf(x)dx=xf(x)-int_{f(0)}^{f(x)}f^{-1}(x)dx$$ or $$ int f(x)dx=xf(x)-int f^{-1}(f(x))df(x)$$ although I'm not sure if the second is valid notation but I think I've seen something like that written before somewhere. These are only valid in ranges where $f(x)$ is bijective. For example: $$be...

up vote 0 down vote favorite I have a chart inside of a card. When being viewed on small or xs screen, I'd like for the card to be hidden but for the chart to still continue to be displayed. I can hide the card easy enough through bootstrap with "d-none d-sm-block", but it makes the chart disappear as well. I was hoping I could simply override the outer div command by placing "d-block" in the chart div, but it does not appear to be that simple. So does anybody know how I can continue to show the inner chart div, while hiding the outer card div on smaller screens? I've created a very simplistic jsfiddle that you can resize to see what's going on. <div class="container"> <div class="row"> <div class="card card-cascade wider reverse d-none d-sm-bloc...