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I read in a text book that area Moment of Inertia (M.I.) of any shape would be Ʃ of (y^{2}χ A)1,2...n where,

A represents the Area of strip no. 1, 2... n

y is the distance between globlal centre of gravity (C.G.) of the shape to th local C.G. of strip no. 1, 2... n

(pl. look at the image)

Though I remember the formula for finding M.I. of a rectangle is [bd^{3}/12] where b and d are breadth and depth of the rectangle, I tried doing it experimentally.

That is:

1. I Drew a rectangle.

2. Split it into 4 equal strips.

3. Measured area and the distance between local and global C.G.s.

4. Did Ʃ of (y^{2}χA)1,2,3 and 4.

I didn't get the value equal to the one done using standard formula. Surprisingly, when I did the same exercise but with splitting the rectangle into 8 equal parts, I got a different answer. But this answer went closer to the M.I. by standard formula.

Now, when I try to find the reason myself, I see that the standard formula has been derived using integration. Since, I am pretty bad in math, can somebody pl. explain me the concept of integration with this example? This will help me to understand when to use integration as well. Many thanks in advance!

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# Area moment of inertia calculation without standard formula

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