Saturday, February 28, 2026

Application of double integrals: finding moments about x and y axes

 Objective: Finding moments about x and y axis





Let's find the moments with respect to x and y of a region R with density function ⍴(x,y). We divide the region in small rectangles for which the density is constant. We add the moments of each of these rectangles and take the limit of the sum as as the rectangles approach zero.

If we name Rᵢⱼ the small rectangle, the moment with respect to the x-axis is:




Similarly, the moment with respect to the y-axis is defined by:




Example

We use the same example in a previous blog post




Solution










Practice







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