Application of Integrals 2 marks Questions, CBSE Class 12 PYQs 2024–2026

1 different 2 marks questions on Application of Integrals from CBSE Class 12 Maths board exams 2024–2026, newest first.

Calculate the area of the region bounded by the curve $\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ and the x-axis using integration.

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Answer:

3 π

sq. units

Upper half of the ellipse: $y = \frac{2}{3} 9 - x^{2}$ , $- 3 \leq x \leq 3$ .
Area $= \int_{- 3}^{3} \frac{2}{3} 9 - x^{2} d x = \frac{4}{3} \int_{0}^{3} 9 - x^{2} d x$ .
$= \frac{4}{3} [\frac{x}{2} 9 - x^{2} + \frac{9}{2} sin^{- 1} \frac{x}{3}]_{0}^{3} = \frac{4}{3} \times \frac{9 π}{4} = 3 π$ sq. units.

Application of Integrals: 2 marks Questions (CBSE Class 12)