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