Riemann Sums - Calculus

Question

Answer 1

square root of (9-x^2) is a circle with right and left, minimum points

at x=3, y = 0, the point (3,0) and (-3,0). 0 is the minimum value

y = sqr(9-x^2) is the top half of a circle

y^2 = 9-x^2

x^2 +y^2 = 3^2 is a circle with center at the origin and radius = 3

exact area between the semi circle and the x axis is A/2 = pir^2/2 = 9pi/2 = 4.5pi = about 14.137

Use the formula for the Area of a circe: pi times radius squared. Then divide by 2, to get the area of a semi-circle