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. \(\frac{2}{3}\)
• C. \(\frac{1}{3}\)
• D. \(\frac{4}{3}\)

Hint:

Area under \(y=f(x)\) from \(a\) to \(b\) is \(\int_a^b f(x)\,dx\).

Answer 1

The Correct Option is D

Step 1: Area under curve \(y=4x^2\) from \(x=0\) to \(x=1\) is: \[ A=\int_0^1 4x^2\,dx \]

Step 2: \[ A=4\left[\frac{x^3}{3}\right]_0^1 \]

Step 3: \[ A=\frac{4}{3}(1^3-0^3) \] \[ A=\frac{4}{3} \] \[ \boxed{\frac{4}{3}} \]