CUET · MATHS · PYQ PAPER 2025
The area (in sq. units) of the region bounded by the parabola \(y^2=8 x\) and the line \(x=2\) is
- A \(\frac{32}{3}\)
- B \(\frac{1}{3}\)
- C \(\frac{16}{3}\)
- D \(\frac{4}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{32}{3}\)
Step-by-step Solution
Detailed explanation
Area \(A = 2 \int_{0}^{2} \sqrt{8x} dx\) \(A = 4\sqrt{2} \int_{0}^{2} x^{1/2} dx = 4\sqrt{2} \left[ \frac{x^{3/2}}{3/2} \right]_{0}^{2}\) \(A = \frac{8\sqrt{2}}{3} (2^{3/2} - 0^{3/2}) = \frac{8\sqrt{2}}{3} (2\sqrt{2})\) \(A = \frac{8 \cdot 2 \cdot 2}{3} = \frac{32}{3}\)
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