The area (in sq. units) of the region bounded by the curve \(x^2 = 250y\), \(y = 0\) and \(x = 50\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{500}{3}\)
The parabola \(y = \frac{x^2}{250}\) touches the x-axis at the origin. The region is the area under the curve from \(x = 0\) to \(x = 50\):
\( \displaystyle \text{Area} = \int_{0}^{50} \frac{x^2}{250}\,dx \)
\( \displaystyle = \frac{1}{250}\left[\frac{x^3}{3}\right]_{0}^{50} \)
\( \displaystyle = \frac{125000}{750} = \frac{500}{3} \)