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Computing area with parametrically represented boundaries If the boundary of a figure is represented by parametric equations x = x (t) , y = y(t) , then the area of the figure is evaluated by one of the three formulae S = -int_(alpha)^(beta) y(t) x'(t) dt , S = int_(alpha)^(beta) x (t) y' (t) dt S = (1)/(2) int_(alpha)^(beta) (xy'-yx') dt where alpha and beta are the values of the parameter t corresponding respectively to the beginning and the end of traversal of the contour . The area of the region bounded by the an arc of cycloid x = a (t - sin t) , y = a ( 1 - cost) and the x-axis |
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Answer» `pi a^(2)` |
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