Question

The area bounded by the curve \(y = 4x^2\), the x-axis, the line x=0 and the line x = 1 is

• A. 2
• B. 2/3
• C. 1/3
• D. 4/3

Hint:

Finding the area under a curve is a direct application of definite integration. Always check if the function is above or below the x-axis in the given interval. If the function dips below the x-axis, you'll need to split the integral and take the absolute value of the negative parts to get the total area.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
Find RMS of f(x)=x² on [0,1].

Step 2: Key Formula (Alternate):
RMS = √[(1/(b-a))∫ₐᵇ (f(x))² dx].

Step 3: Detailed Explanation:
(f(x))²=x⁴. Mean square = ∫₀¹ x⁴ dx = [x⁵/5]₀¹ = 1/5. RMS = √(1/5) = 1/√5.

Step 4: Final Answer:
RMS is 1/√5.