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Let S be the area of the region enclosed...

Let `S` be the area of the region enclosed by `y=e^-x^2,y=0,x=0,a n dx=1.` Then `Sgeq1/e` (b) `Sgeq1=1/e` `Slt=1/4(1+1/(sqrt(e)))` (d) `Slt=1/(sqrt(2))+1/(sqrt(e))(1-1/(sqrt(2)))`

A

`Sge1/e`

B

`Sge1-1/e`

C

`Sle1/4(1+1/(sqrt(e)))`

D

`Sle1/(sqrt(2))+1/(sqrt(e))(1-1/(sqrt(2)))`

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The correct Answer is:
B, D
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If S be the area of the region enclosed by y=e^(-x^(2)), y=0, x=0 and x = 1. Then :

Let S be the area of the region enclosed by y=e^(-x^(2)),y=0,x=0, and x=1. Then (a) S>=(1)/(e)( b) S>=1=(1)/(e)(c)S<=(1)/(4)(1+(1)/(sqrt(e))) (d) S<=(1)/(sqrt(2))+(1)/(sqrt(e))(1-(1)/(sqrt(2)))

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ARIHANT MATHS-AREA OF BOUNDED REGIONS-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. The area enclosed by the curvesy= sinx+cosx and y = | cosx-sin x | ove...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. The area bounded by the curves y=cosx and y=sinx between the ordinates...

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

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