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"If "f: [-1,1]rarr[-(1)/(2),(1)/(2)],f(x...

`"If "f: [-1,1]rarr[-(1)/(2),(1)/(2)],f(x)=(x)/(1+x^(2)),` then find the area bounded by `y=f^(-1)(x), x` axis and lines `x=(1)/(2), x=-(1)/(2).`

A

`1/2 log e`

B

`log(e/2)`

C

`1/2 log e/3`

D

`1/2 log (e/2)`

Text Solution

Verified by Experts

The correct Answer is:
B
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ARIHANT MATHS-AREA OF BOUNDED REGIONS-Exercise (Single Option Correct Type Questions)
  1. A point P(x,y) moves such that [x+y+1]=[x]. Where [.] denotes greatest...

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  2. "If "f: [-1,1]rarr[-(1)/(2),(1)/(2)],f(x)=(x)/(1+x^(2)), then find the...

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  3. If the length of latusrectum of ellipse E(1):4(x+y+1)^(2)+2(x-y+3)^(2)...

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  4. The area of bounded by the curve 4|x-2017^(2017)|+5|y-2017^(2017)|larr...

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  5. If the area bounded by the corve y=x^(2)+1, y=x and the pair of lines ...

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  6. Suppose y=f(x) and y=g(x) are two continuous functiond whose graphs in...

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  7. Let 'a' be a positive constant number. Consider two curves C1: y=e^x...

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  8. 3 point O(0,0),P(a,a^2),Q(-b,b^2)(agt0,bgt0) are on the parabola y=x^2...

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  9. Area enclosed by the graph of the function y= In^2x-1 lying in the 4...

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  10. The area bounded by y = 2-|2-x| and y=3/|x| is

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  11. Suppose g(x)=2x+1 and h(x)=4x^(2)+4x+5 and h(x)=(fog)(x). The area enc...

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  12. The area bounded by the curves y=-sqrt(-x) and x=-sqrt(-y) where x,yle...

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  13. y=f(x) is a function which satisfies f(0)=0, f"''(x)=f'(x) and f'(0)=1...

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  14. Aea of the region nclosed between the curves x=y^2-1 and x=|y|sqrt(1-y...

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  15. The area bounded by the curve y=xe^(-x);xy=0and x=c where c is the x-c...

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  16. If (a,0), agt 0, is the point where the curve y=sin 2x-sqrt3 sin x cut...

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  17. The curve y=ax^2+bx +c passes through the point (1,2) and its tangent ...

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  18. A function y=f(x) satisfies the differential equation (dy)/(dx)-y= co...

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  19. If the area bounded between X-axis and the graph of y=6x-3x^2 between ...

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  20. Area bounded by y=f^(-1)(x) and tangent and normal drawn to it at poin...

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