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If the boundary of figure is represented by parametric equations i.e. x = x (t), y = y (t), then the area of the figure is evaluated by one of the three formulas S = - underset(alpha)overset(beta)(int)y(t) x' (t) dt,S = underset(alpha)overset(beta)(int) x(t). y'(t) dt S = (1)/(2) underset(alpha)overset(beta)(int) (xy' - yx') dt where alpha and beta are the values of the parameter t corresponding respectively to the beginning and the end of of the traversal of the curve corresponding to increasing t The area enclose by the asteroid ((x)/(a))^(z//3) + ((y)/(a))^(2//3) = 1 is |
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Answer» `(3)/(4) a^(2) pi` |
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