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Hello,, I'm reading about beams in mechanics of matrials. But I'm a bit stuck because of one thing that I either don't understand or just don't comply with!

So, here's a picture from the book: picture 003

It says that the center of mass should be at 2/3 of the length..

I tried to calculate the center of mass on my own using integrals which states that it should be L/√2

here's my solution using a and b instead of L, am I doing something wrong? : pisture 004

So, here's a picture from the book: picture 003

It says that the center of mass should be at 2/3 of the length..

I tried to calculate the center of mass on my own using integrals which states that it should be L/√2

here's my solution using a and b instead of L, am I doing something wrong? : pisture 004

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