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Consider the function defined implicitly...

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-valued diferentiable function `y-g(x)` satisfying `g_(0)=0`.
`int_(-1)^(1)g'(x)dx` is equal to

A

`2g(-1)`

B

0

C

`-2g(1)`

D

`2g(1)`

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The correct Answer is:
D
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ARIHANT MATHS-AREA OF BOUNDED REGIONS-Exercise (Questions Asked In Previous 13 Years Exam)
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  7. Find the product of (x - 4)(x - 7)

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  8. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

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  9. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

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  10. The area (in sqaure units) of the region {(x,y):x ge 0, x + y le 3, x^...

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  11. The area (in sq. units) of the region {(x,y):y^(2)ge2x and x^(2)+y^(2)...

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  12. The area (in sq units) of the region described by {(x,y):y^(2)le2x and...

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  13. The area (in sq. units) of the quadrilateral formed by the tangents ...

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  14. The area of the region described by A={(x,y):x^(2)+y^(2)le1 and y^(2)l...

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  15. The area bounded by the curves y=sqrt(x),2y+3=x , and x-axis in the 1s...

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  16. The area bounded between the parabolas x^(2)=(y)/(4) and x^(2)=9y and ...

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  17. The area of the region enclosed by the curves y=x, x=e,y=(1)/(x) and t...

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  18. The area bounded by the y-axis, y = cosx, and y = sinx when 0<x<π/2 is...

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  19. The area of the region bounded by the parabola (y-2)^(2) = x- 1, the t...

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  20. The area of the plane region bounded by the curves x""+""2y^2=""0 and ...

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