Question

The RMS value of \(x^2\) in [0, 1] is

• A. \(\frac{1}{\sqrt{5}}\)
• B. \(\frac{1}{5}\)
• C. \(\frac{1}{\sqrt{3}}\)
• D. \(\frac{1}{3}\)

Hint:

Remember the three steps for RMS: Square the function, find the Mean (average) of the result over the interval, and then take the square Root. Following the steps in reverse order (S-M-R) helps in remembering the process.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
Find degree of y'+y=5/y'.

Step 2: Key Formula (Alternate):
Multiply by y' to clear fraction. Highest power of highest order derivative = degree.

Step 3: Detailed Explanation:
y'(y'+y)=5 → (y')²+yy'=5. Highest derivative is y' (order 1). Its highest power is 2. Degree=2.

Step 4: Final Answer:
Degree is 2.