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Let A(n) between area bounded by the cur...

Let `A_(n)` between area bounded by the curve `y=(tan x)^(n),n in N` and the lines y = 0 and `x=(pi)/(4)`. For `n gt 2`, prove that `A_(n)+A_(n-2)=(1)/(n-1)` and decuce that `(1)/(2n+2)lt A_(n)lt (1)/(2n-2)`

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AAKASH SERIES-AREAS-ADDITIONAL EXERCISE
  1. The area common to the circle x^2+y^2=64 and the parabola y^2=12x is e...

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  2. Compute the area of the region bounded by the straight lines x = 0, x ...

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  3. The area of the region bounded by the curves y=x^(2)andy=(2)/(1+x^(2))...

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  4. The area bounded by the curves y=xe^(x),y=xe^(-x) and line x=1, is

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  5. The area of the region bounded by the curves y=|x-1|andy=3-|x| is

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  6. Find the area of the region bounded by the curves x=|y^(2)-1| and y=x-...

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  7. Find the are of the region bounded by y= log(e )x and y= sin^(4) (pi x...

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  8. Find the area of the region bounded by 4y=|4-x^(2)| and y=7-|x|

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  9. Find the area enclosed by y=log(e)(x+e) and x=log(e)((1)/(y)) and the ...

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  10. Let f(x)=" max "{sin x, cos x, (1)/(2)}. Determine the area of the reg...

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  11. Let f(x)=" max "{x^(2),(1-x)^(2),2x(1-x)} where 0le x le 1. Determine ...

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  12. Let A(n) between area bounded by the curve y=(tan x)^(n),n in N and th...

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  13. Find the area enclosed between the curves y^(2)=2x,y=4x-1

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  14. Find the area enclosed between the curves y^(2)=2x+6 and y=x-1

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  15. Find the area enclosed between the curves y=4x^(2) and y=x^(2)+3

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  16. Find the area enclosed between the curves y=x^(2),y=2x-x^(2)

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  17. Find the area of the region formed by the segment cut off from the par...

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  18. Find the area of the region bounded by y^(2)=4ax between the lines x=a...

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  19. The area of the region bounded by the curve sqrtx+sqrty=sqrta(x,ygt0) ...

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  20. Find the area of the region in the first quadrant enclosed by the x-ax...

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