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Problem 72 Hard Difficulty

The linear density of a rod of length $ 1\;m $ is given by $ p(x) = 1/\sqrt{x} $, in grams per centimeter, where $ x $ is measured in centimeters from one end of the rod. Find the mass of the rod.

Answer

$$
20 \mathrm{g}
$$

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Video Transcript

for this problem here we are asked to um if the linear density of a rod of length, one m is given to us as p of X equals one over root X. We want to know the mass of the rod. So to find mass of the rod, we're going to um consider the fact that mask will be the anti derivative of this. So our density is equal to X to the negative one half. Um so when we solve this for an index, that committee anti derivative, which will give us to root X plus some constant. And we know the mass should be zero. X equals zero. So that would be a good point to test. And that I would just give us that the constant value of zero. So our final mass function is going to be to root X. Therefore, if we plug in 100 centimeters for the one m rod, we would get and of 100 which would give us 20. So therefore our masses 20 grands.