Geometrical integral interpretation

[miloslavc]

Hi friends, i have i request for you. For my statics exam i need integrals and i found this page in russian, and can not find rest or even know how it's called because when i translate title i don't get any results. Can you please help me and tell me where can i find the rest. https://app.box.com/s/k9a15wb6bit4ezpp25r7

 

[tiny-tim]

welcome to pf!

hi miloslavc! welcome to pf!

i don't recognise any of those results, but the formula might be a product of inertia (an off-diagonal component of a moment of inertia or moment of area tensor)

 

[SteamKing]

IDK about the integrals being products of inertia, but the table represents the value of the integral of the products of two different distributions. Across the top, you have a triangular and a trapezoidal distribution, Mi. Down the left hand side, you start with a trapezoidal, triangular, then a constant distribution, Mk. The values within the table are for the integral of the combined distribution Mi*Mk.

I'm not sure, but I think such a table would be used in calculating things like area-moment diagrams. Instead of finding the product of the two distributions using point-by-point multiplication and then integrating, the table gives the value of a particular combination expressed in terms of quantities of the component distributions.

When the OP says 'For my statics exam, I need integrals.', what the heck does that mean?