CUET · MATHS · PYQ PAPER 2025
The area (in sq.units) of region bounded by \(y^2=9 x, x=2, x=4\) and the \(x\)-axis in the first quadrant is
- A \(3[4-\sqrt{2}]\)
- B \(2[4+\sqrt{2}]\)
- C \(8[4-\sqrt{2}]\)
- D \(4[4-\sqrt{2}]\)
Answer & Solution
Correct Answer
(D) \(4[4-\sqrt{2}]\)
Step-by-step Solution
Detailed explanation
The region is bounded by \(y = \sqrt{9x} = 3\sqrt{x}\). Area \(A = \int_{2}^{4} 3\sqrt{x} \,dx\) \(A = 3 \left[ \frac{x^{3/2}}{3/2} \right]_{2}^{4} = 2 [x^{3/2}]_{2}^{4}\) \(A = 2 (4^{3/2} - 2^{3/2}) = 2 (8 - 2\sqrt{2})\) \(A = 16 - 4\sqrt{2} = 4(4 - \sqrt{2})\) sq.units.
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