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Answer (I = (1/8) M L^2)

This problem is totally throwing me off. Normally lambda is equal to (M/L) so im not sure what this new formula is doing to the problem. I tried substituting and came up with (1/32)ML^3 which is horribly off from the answer. My idea was to add the x term from the new lambda giving me x^3. I then brought lambda (sub zero) out of the integral and integrated from (-L/2) to positive (L/2). Which brings us back to the wrong answer. Any ideas as to where I’m going wrong would be much appreciated!

Thanks

Dan