Enclosed Parts
December 1st, 2007
Calculus involving integration. You have to split area into two equal parts?
the problem:
Find a vertical line: x=k that divides the area enclosed by x=sq.rt(y), x=12 and y=0 and into two equal parts.
I graphed it, but now what? Please show your work. Any help is greatly appreciated.
x = sqrt(y)
y = x^2
int(x^2 dx , x = 0 ,x = k) = int(x^2 dx , x = k , x = 12)
(k^3 / 3) = 12^3 / 3 – k^3 / 3
2 * k^3 / 3 = 12^3 / 3
2 * k^3 = 12^3
k^3 = (1728 / 2)
k = 12 / (2)^(1/3)
k = 9.5244063118091968485102338356338
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