Calculus Need help please!

Question

Use geometry to evaluate  . (4 points)

Answer Choices:

	π
	2π
	Cannot be evaluated

Answer 1

y = √(4 - x²) [squaring both sides we get:

y² = 4 - x² [adding x² to both sides we get:

x² + y² = 4

You probably recognize this as the equation of a circle centered at the origin with a radius of 2. But since the original equation is the positive square root, this is just the top half of the circle.

Using geometry, the area of a circle is πr² so, since this is half a circle, the area under the curve (or the integral) is 1/2πr² = 1/2π(2)² = 2π