The area (in sq. units) of the region bounded by the curve \(y = 3x^{2}\), the x-axis and the lines x = 0 and x = 3 is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 27
Since \(3x^{2} \ge 0\), the curve lies above the x-axis, so the area is the integral of y from x = 0 to x = 3:
\( \displaystyle A = \int_{0}^{3} 3x^{2}\,dx \)
\( \displaystyle = \left[x^{3}\right]_{0}^{3} \)
\(= 27 - 0 = 27\)