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Consider the functions defined implicitl...

Consider the functions defined implicitly by the equation` y^(3) – 3y + x = 0 `on various intervals in the real line. If `x in (–infty , –2) cup (2, infty)`, the equation implicitly defines a unique real valued differentiable function `y = f(x). If x in (–2, 2)`, the equation implicitly defines 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 `– infty lt a lt b lt – 2,` is

A

`int_(a)^(b) x/(3((f(x))^(2)-1))dx + bf(b) - af(a)`

B

`-int_(a)^(b) x/(3((f(x))^(2)-1))dx + bf(b) - af(a)`

C

`int_(a)^(b) x/(3((f(x))^(2)-1))dx - bf(b) + af(a)`

D

`-int_(a)^(b) x/(3((f(x))^(2)-1))dx - bf(b) + af(a)`

Text Solution

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The correct Answer is:
A
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