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CUET · MATHS · PYQ PAPER 2023

The area under the curve \(y=2 \sqrt{2 a x}\) bounded by the lines \(x-4=0\) and \(y=0\) is \((a>0)\) :

  1. A \(\frac{16 \sqrt{2 a}}{3}\) sq. units
  2. B \(\frac{8 \sqrt{2 a}}{3}\) sq. units
  3. C \(\frac{64 \sqrt{2 a}}{3}\) sq. units
  4. D \(\frac{32 \sqrt{2 a}}{3}\) sq. units
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{32 \sqrt{2 a}}{3}\) sq. units

Step-by-step Solution

Detailed explanation

\(A = \int_{0}^{4} 2 \sqrt{2 a x} \, dx\) \(A = 2 \sqrt{2a} \int_{0}^{4} x^{1/2} \, dx = 2 \sqrt{2a} \left[ \frac{2}{3} x^{3/2} \right]_{0}^{4}\) \(A = 2 \sqrt{2a} \left( \frac{2}{3} (4)^{3/2} \right) = 2 \sqrt{2a} \left( \frac{2}{3} \cdot 8 \right) = \frac{32 \sqrt{2a}}{3}\)