The area (in sq. units) of the region bounded by the curve \(y = 6x^{2}\), the x-axis and the lines x = 1 and x = 2 is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 14
Since \(6x^{2} \ge 0\), the curve lies above the x-axis, so the area is the area under the curve from x = 1 to x = 2:
\( \displaystyle A = \int_{1}^{2} 6x^{2}\,dx \)
\( \displaystyle = \left[2x^{3}\right]_{1}^{2} \)
\( = 16 - 2 = 14 \)