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Consider the functions defined implicitly by the equationy^(3)-3y+x=0 on various intervals in the real line. If x in (-oo, -2)uu(2, oo), the equation implicitly defines a unique real-valued differentiable function y=f(x). If x in (-2, 2), the equation implicitlydefines a unique real-valued differentiable function y=g(x) satisfying g(0)=0. The area of the region bounded by the curve y=f(x), the X-axis and the lines x = a and x = b, where - oo lt a lt b lt -2, is : |
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Answer» `int_(a)^(b)(x)/(3[{F(x)}^(2)-1])dx + BF(b)-AF(a)` |
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