Based on the following given information answer the question
Consider the function \(f(x) = x|x|\), \(x \in \mathrm{R}\).
The area of the region bounded by \(f(x) = x|x|\) and x-axis from x = 0 to x = 4 is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\displaystyle\frac{64}{3}\) sq. units
For \(x \ge 0\), |x| = x, so \(f(x) = x^{2} \ge 0\) and the curve lies above the x-axis. The area is
\( \displaystyle \int_{0}^{4} x^{2}\,dx = \left[\frac{x^{3}}{3}\right]_{0}^{4} \)
\( \displaystyle = \frac{64}{3} \text{ sq. units} \)