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Definite Integration question

2008 · Shift 1 · Q29

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PYQ Library
JEE Advanced
Mathematics
Definite Integration
2008 · Shift 1 · Q29

Definite Integration question

2008 · Shift 1 · Q29

JEE AdvancedMathematicsDefinite IntegrationMCQ+3 / −1

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

\int\limits_{ - 1}^1 {g'\left( x \right)dx = }

A
$2g(-1)$
B
$0$
C
$-2g(1)$
D
$2g(1)$

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