Use equation I=∫r2dm to calculate the moment of inertia of a slender, uniform rod with mass M and length L about an axis at one end, perpendicular to the rod. Express your answer in terms of the variables M and L.

The moment of inertia is    

Explanation:

From the question we a given an equation

Now let look at a small length da of this uniform rod that a meters form the x-axis

 The mass of this small section can be mathematically evaluated as

For this small portion for the rod the moment of inertia is

Substituting for dM

to get I we integrate both sides

the answer is b ) square root of 5

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