CUET · MATHS · PYQ PAPER 2025
The area of the region bounded by the curves \(y=x^2+2\) and the \(x\)-axis, between \(x=0\) and \(x=3\) in the first quadrant is :
- A \(\frac{16}{3}\) sq.units
- B 15 sq.units
- C \(\frac{21}{2}\) sq.units
- D 12 sq.units
Answer & Solution
Correct Answer
(B) 15 sq.units
Step-by-step Solution
Detailed explanation
\(A = \int_{0}^{3} (x^2+2) \,dx\) \(A = \left[ \frac{x^3}{3} + 2x \right]_{0}^{3}\) \(A = \left( \frac{3^3}{3} + 2(3) \right) - \left( \frac{0^3}{3} + 2(0) \right)\) \(A = (9 + 6) - (0)\) \(A = 15\)
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