Find the Root Mean Square of the function f(x) = 2x+3 on the interval [1, 4].

Step 1 ：Step 1: The formula for the Root Mean Square (RMS) of a function on the interval [a, b] is \( RMS = \sqrt{\frac{1}{b-a} \int_{a}^{b} [f(x)]^2 dx} \). Here, f(x) = 2x + 3, a = 1, and b = 4.

Step 2 ：Step 2: First, calculate \([f(x)]^2\). This is \((2x + 3)^2 = 4x^2 + 12x + 9\).

Step 3 ：Step 3: Next, calculate the integral of \([f(x)]^2\) from 1 to 4. This is \( \int_{1}^{4} (4x^2 + 12x + 9) dx = [\frac{4}{3}x^3 + 6x^2 + 9x]_{1}^{4} = \frac{4}{3}*64 + 6*16 + 9*4 - (\frac{4}{3}*1 + 6*1 + 9*1) = 256/3 + 96 + 36 - 20/3 = 348.\)

Step 4 ：Step 4: Finally, substitute these values into the RMS formula to get \( RMS = \sqrt{\frac{1}{4-1} * 348} = \sqrt{116} \approx 10.77.\)