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Let `A_n` be the area bounded by the curve `y=(tanx)^n` and the lines `x=0,y=0,` and `x=pi/4dot` Prove that for `n >2,A_n+A_(n-2)=1/(n-1)` and deduce `1/(2n+2)

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The correct Answer is:
`(1)/(2(n+1)) < A_(n) < 1/(2(n-1))`
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ARIHANT MATHS-AREA OF BOUNDED REGIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let An be the area bounded by the curve y=(tanx)^n and the lines x=0,y...

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  2. Area of region {(x,y) in R^(2): y ge sqrt(|x+3|,)5y le x + 9 le 15}

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  3. Let F(x)=intx^[x^2+pi/6][2cos^2t.dt] for all x in R and f:[0,1/2] -> [...

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  4. The common tangents to the circle x^2 + y^2 =2 and the parabola y^2 = ...

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  5. The area enclosed by the curvesy= sinx+cosx and y = | cosx-sin x | ove...

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  6. Let S be the area of the region enclosed by y=e^-x^2,y=0,x=0,a n dx=1....

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  7. Let f:[-1,2]vec[0,oo) be a continuous function such that f(x)=f(1-x)fo...

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  8. Let the straight line x= b divide the area enclosed by y=(1-x)^(2),y=0...

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  9. Area of the region bounded by the curve y=e^(x) and linesx=0 and y=e i...

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  10. The area of the region bounded by the curves y=sqrt[[1+sinx]/cosx] and...

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

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

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

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

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

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

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

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  18. The area of the region described by A = {(x,y) : x^2 + y^2 lt= 1and y^...

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  19. The area (in square units) bounded by the curves y=sqrt(x),2y-x+3=0, x...

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  20. The area bounded between the parabola x^(2)=y/4 and x^(2)=9y and the s...

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

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