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Consider the function defined implicitly by the equation y^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 defferentiable function y=f(x). If x in (-2,2), the equation implicitly defines a unique real-valud diferentiable 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 line 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+by(b)-af(a)` |
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