Find the area of the circle x² + y² = a² using the method of integration.

Model Answer & Options

Source: Extra Practice

πa² sq. units

2πa² sq. units

πa²/2 sq. units

4πa² sq. units

Explanation

Area = 4 * ∫[0 to a] √(a² - x²) dx (considering the first quadrant). Using the standard formula ∫√(a² - x²) dx = (x/2)√(a² - x²) + (a²/2)sin⁻¹(x/a), we evaluate from 0 to a. At x=a, it's (a²/2)(π/2) = πa²/4. Multiplying by 4 gives πa². Options B, C, and D are incorrect multiples of the area of a circle.

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