Question

Calculate the average height above the x-axis of a point in the region

Answer 1

dA = dy dx
....................1....x²
S = ∫ y dA = ∫.... ∫ y dy dx
..................0....0

......1
S = ∫ ½ x⁴ dx
.....0

S = 0.1 x^5 = 0.1 (1)^5 = 0.1



dA = dy dx

......1.x²
A = ∫ ∫ 1 dy dx
.....0 0


......1.
A = ∫ x² dx
.....0

A = ⅓ x³ = ⅓ (1)³ = ⅓

y = S/A = (0.1)(3)

y = 0.3