Home
Class 12
MATHS
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` and `x=1`. Then

A

`S ge 1/e`

B

`S ge 1 - 1/e`

C

`S le 1/4 (1+(1)/(sqrt(e )))`

D

`S le 1/(sqrt(2)) + 1/(sqrt(e ))(1-1/(sqrt(2)))`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 3 Part - II|25 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise High Level Problem|26 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 2 Part - IV|6 Videos

  • COMBINATORICS

    RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos

  • DPP

    RESONANCE ENGLISH|Exercise QUESTION|656 Videos

Similar Questions

Explore conceptually related problems

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 (c) Slt=1/4(1+1/(sqrt(e))) (d) Slt=1/(sqrt(2))+1/(sqrt(e))(1-1/(sqrt(2)))

Find the area of the region bounded by y =x^(2)+1 ,y=x ,x=0 and y=2

The area of the region bounded by y=x^(2)+2,y=-x,x=0 and x = 1 is

The area of the region enclosed by y=x^2 and y=sqrt(|x|) is

The area of the figure bounded by y=e^(x-1),y=0,x=0 and x=2 is

Find the area of the region bounded by y=-1,y=2, x=y^3 and x=0.

Find the area of the region enclosed by the curves y=x^(2) and y = 2x

Find the area of the region enclosed by the curves y=x^(2) and y=x^(3)

Find the area of the region enclosed by y=-5x-x^(2) and y=x on interval [-1,5]

The area of the region bounded by x^(2)+y^(2)-2x-3=0 and y=|x|+1 is

RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I
  1. Let the straight line x= b divide the area enclosed by y=(1-x)^(2),y=0...

    Text Solution

    |

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

    Text Solution

    |

  3. Let S be the area of the region enclosed by y-e^(-x^(2)),y=0, x=0 and ...

    Text Solution

    |

  4. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

    Text Solution

    |

  5. Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = in...

    Text Solution

    |

  6. Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = in...

    Text Solution

    |

  7. If f(x) = int(0)^(x) e^(t^(2)) (t-2) (t-3) dt for all x in (0, oo) , t...

    Text Solution

    |

  8. The area enclosed by the curve y=sinx+cosxa n dy=|cosx-sinx| over the ...

    Text Solution

    |

  9. Let f:[1/2,1]vecR (the set of all real numbers) be a positive, non-con...

    Text Solution

    |

  10. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...

    Text Solution

    |

  11. Let f:[a,b]to[1,oo) be a continuous function and let g:RtoR be defined...

    Text Solution

    |

  12. Let f:(0,oo)vecR be given by f(x)=int(1/x)^x(e^(-(t+1/t))dt)/t , then ...

    Text Solution

    |

  13. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dx is

    Text Solution

    |

  14. The following integral int(pi//4)^(pi//2)(2cosec x)^(17) dx dx is equa...

    Text Solution

    |

  15. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

    Text Solution

    |

  16. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

    Text Solution

    |

  17. ((int(-1/2)^(1/2)cos 2x *log((1+x)/(1-x))dx))/((int(0)^(1/2)cos 2x *lo...

    Text Solution

    |

  18. Let f: RvecR be a function defined by f(x)={[x],(xlt=2) \ \ (0,x >2) ...

    Text Solution

    |

  19. If alpha=int0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx where tan^(-1)...

    Text Solution

    |

  20. Let f: R rarr R be a continuous odd function, which vanishes exactly a...

    Text Solution

    |