Learn how to evaluate the definite integral by graphing a semi circle

The video tutorial explains how to rewrite an equation to identify it as a circle equation, with a center at (0,0) and a radius of 2. It further discusses how this equation represents a semicircle, focusing on the positive form. The tutorial concludes by calculating the area of the semicircle, using the formula for the area of a circle and adjusting it for the semicircle.

What is the center and radius of the circle represented by the equation y^2 + x^2 = 4?

• Center: (2,2), Radius: 2

• Center: (0,0), Radius: 2

• Center: (1,1), Radius: 4

• Center: (0,0), Radius: 4

What does the equation y = sqrt(4 - x^2) represent in terms of the circle?

• The negative half of the circle

• The positive half of the circle

• The entire circle

• A line tangent to the circle

What is the range of x-values considered for the semicircle in the video?

• -3 to 3

• -2 to 2

• 0 to 2

• -4 to 4

How is the area of the semicircle calculated?

• 1/2 * π * r^2

• 2 * π * r

• π * r^2

• π * r

What is the final calculated area of the semicircle?

• 4π

• π

• 2π

• 3π