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CBSE Class 12 · 2006 · Definite IntegralsVery Short Answer

\int_{0}^{2} 4 - x^{2} d x

Answer: $π$

Solution

The integrand is the upper half of the circle

x^{2} + y^{2} = 4

of radius

2

, so the value is the area of a quarter disc. Evaluating by the standard formula:

\int_{0}^{2} 4 - x^{2} d x = [\frac{x}{2} 4 - x^{2} + \frac{4}{2} sin^{- 1} \frac{x}{2}]_{0}^{2}

= (0 + 2 \cdot \frac{π}{2}) - (0 + 0) = π

Final answer:

π

.

CBSE Class 12 Board · 2006 · Subjective

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