Please help me on calculus - integral

Question

Use geometry to evaluate 

Options:

1. π/2
2. π
3. 2π
4. Cannot be evaluated

Answer 1

The graph of y = √(4 - x²), where -2 ≤ x ≤ 2 is the upper half of the circle with center (0,0) and radius 2.

So, ∫_{(-2 to 2)} √(4 - x²)dx = (1/2)(Area of circle) = (1/2)(π(2)²) = 2π.