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Estimate the area under the curve of y equals x squared for 0 is less than or equal to x and 3 is greater than or equal to x?
Wiki User
∙ 13y ago
The area of the region enclosed by the line x = 3, x-axis, and the parabola y = x2.
y = x2, 0 ≤ x ≤ 3
y = x2 or x = √y
x = √y
x = 3
√y = 3
y = 9 (so the points of intersection is (3, 9))
A = integral from 0 to 9 of (3 - y1/2) dy
= (3y - (2/3)y3/2)|0,9
= 3(9) - (2/3)(93/2)
= 27 - (2/3)(36/2)
= 27 - (2/3)(33)
= 27 - 18 = 9
Wiki User
∙ 13y ago
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