Find the exact area under the curve between the indicated values of $x$. $y=\frac{3}{x^{3}}$, between $x=1$ and $x=3$ A. $\frac{1}{2}$ B. 3 C. $\frac{1}{3}$ D. $\frac{4}{3}$

Step 1 ：We are given the function \(y=\frac{3}{x^{3}}\) and we are asked to find the exact area under the curve between \(x=1\) and \(x=3\).

Step 2 ：To find the exact area under the curve, we need to integrate the function from the lower limit to the upper limit.

Step 3 ：The integral of \(\frac{3}{x^{3}}\) is \(-\frac{3}{2x^{2}}\).

Step 4 ：We will evaluate this at \(x=3\) and \(x=1\) and subtract the two results to find the area.

Step 5 ：The result of the integration is \(\frac{4}{3}\), which is the exact area under the curve between \(x=1\) and \(x=3\).

Step 6 ：Final Answer: \(\boxed{\frac{4}{3}}\)