CUET · MATHS · PYQ PAPER 2025
The area of the region enclosed between the parabola \(y=\frac{3 x^2}{4}\) and the line \(3 x-2 y=12\) is,
- A 63 sq. units
- B 36 sq. units
- C 27 sq. units
- D 18 sq. units
Answer & Solution
Correct Answer
(C) 27 sq. units
Step-by-step Solution
Detailed explanation
\(\frac{3x^2}{4} = \frac{12-3x}{2}\) \(3x^2 = 24-6x\) \(3x^2+6x-24=0\) \(x^2+2x-8=0\) \((x+4)(x-2)=0\) \(x=-4, x=2\) \(A = \int_{-4}^{2} \left( \frac{12-3x}{2} - \frac{3x^2}{4} \right) dx\) \(A = \int_{-4}^{2} \left( 6 - \frac{3}{2}x - \frac{3}{4}x^2 \right) dx\)…
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