If the area (in sq. units) of the region bounded by the curve \(y = x^{2}\), the x-axis and the line x = k, where k > 0, is 9, then k is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 3
The parabola touches the x-axis at the origin, so the region runs from x = 0 to x = k:
\( \displaystyle A = \int_{0}^{k}x^{2}\,dx = \frac{k^{3}}{3} \)
Setting the area equal to 9:
\( \displaystyle \frac{k^{3}}{3} = 9 \)
\(k^{3} = 27\)
\(k = 3\)