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CUET · MATHS · PYQ PAPER 2025

The area of region bounded by the curve \(y^2=4 a x\) and the straight line \(x=2 a, a>0\) in the first quardant is:

  1. A \(\frac{8 a^3}{3}\) sq. units
  2. B \(\frac{8 \sqrt{2} a^2}{3}\) sq. units
  3. C \(\frac{32 a^3}{3}\) sq. units
  4. D \(\frac{64 a^3}{3}\) sq. units
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{8 \sqrt{2} a^2}{3}\) sq. units

Step-by-step Solution

Detailed explanation

\(A = \int_{0}^{2a} 2\sqrt{ax} \, dx\) \(A = 2\sqrt{a} \int_{0}^{2a} x^{1/2} \, dx\) \(A = 2\sqrt{a} \left[ \frac{x^{3/2}}{3/2} \right]_{0}^{2a}\) \(A = \frac{4\sqrt{a}}{3} [(2a)^{3/2} - 0^{3/2}]\) \(A = \frac{4\sqrt{a}}{3} (2^{3/2} a^{3/2})\)…