Find the area under the given curve over the indicated interval. \[ y=2 x ; \quad x=3 \text { to } x=6 \]

Step 1 ：We are given the function \(y = 2x\) and we are asked to find the area under the curve from \(x = 3\) to \(x = 6\).

Step 2 ：The area under a curve from a to b is given by the definite integral from a to b of the function. In this case, the function is \(y = 2x\) and the interval is from \(x = 3\) to \(x = 6\).

Step 3 ：We can calculate this using the formula for the definite integral: \(\int_{a}^{b} f(x) dx\) where \(f(x)\) is the function and a and b are the limits of integration. In this case, \(f(x) = 2x\), a = 3, and b = 6.

Step 4 ：Calculating the definite integral, we find that the area under the curve is 27 square units.

Step 5 ：Final Answer: The area under the curve is \(\boxed{27}\) square units.