Home
Class 12
MATHS
if m and M are the smallest and greatest...

if m and M are the smallest and greatest values of a function f(x) defined on an interval [a,b]then`m(b-a)leint_a^bf(x)dxleM(b-a)`,(i) `f(x)ge0,[a,b]implies int_a^bf(x)dxge0`
`f(x)leg(x),`f(x)leg(x)[a,b]impliesint_a^bf(x)dxleint_a^bg(x)dx`,
Let `g(x)=int_0^xf(t)dt` where `1/2lef(t)le1`,`tin[0,1]` and `0lef(t)le1/2` for `tin[1,2]` then

A

`-3/2leg(2)lt1/2`

B

`0leg(2)lt2`

C

`-3/2ltg(2)le5/2`

D

`2ltg(2)lt4`

Text Solution

Verified by Experts

The correct Answer is:
2
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY & DIFFERENTIABILITY

    PATHFINDER|Exercise QUESTION BANK|13 Videos

  • DETERMINATES

    PATHFINDER|Exercise QUESTION BANK|21 Videos

Similar Questions

Explore conceptually related problems

Let g(x) =int_0^x f(t) dt where f is such that 1//2lef(t)le1 for tin[0, 1] and 0 lef(t) le1//2 for tin[1, 2] Then the interval in which g(2) lies.

Let g(x)=int_0^x f(t).dt ,where f is such that 1/2<=f(t)<=1 for t in [0,1] and 0<=f(t)<=1/2 for t in [1,2] .Then g(2) satisfies the inequality

Let f(x)=int_(1)^(x)(3^(t))/(1+t^(2))dt , where xgt0 , Then

If f(x)=int_0^x(sint)/t dt ,x >0, then

A Function f(x) satisfies the relation f(x)=e^x+int_0^1e^xf(t)dtdot Then (a) f(0) 0

The function f(x) is defined in 0 le x le1, find the domain of definition of f(2x-1)

The function f(x) is defined in 0 le x le1, find the domain of definition of f(x^2)

If m is the least value (global minimum) and M is the greatest value (global maximum) of the function f(x) on the interval [a , b] (estimation of an integral), then m(b-a)lt=int_a^bf(x)dxlt=M(b-a)dot

Let g(x) = int_(x)^(2x) f(t) dt where x gt 0 and f be continuous function and 2* f(2x)=f(x) , then

PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
  1. Definite integral of any discontinuous or non diffrentiable function i...

    Text Solution

    |

  2. if m and M are the smallest and greatest values of a function f(x)defi...

    Text Solution

    |

  3. if m and M are the smallest and greatest values of a function f(x) def...

    Text Solution

    |

  4. let F(x)=int0^x(2t div1)/(t^2-2t+2)dt,x in[-1,1] then

    Text Solution

    |

  5. Text Solution

    |

  6. I=int0^2x[2x]dx where [.] denotes the greatest integer function then t...

    Text Solution

    |

  7. If pi/2ltalphalt(2pi)/3 and I=int 0^(sin2alpha)dx/sqrt(4cos^2alpha-x^2...

    Text Solution

    |

  8. if int0^(x^2(1+x))f(t)dt=x then the value of 10f(2) must be

    Text Solution

    |

  9. f(x)=int1^xlogt/(1+t+t^2)dt (xge1) then prove that f(x) =f(1/x)

    Text Solution

    |

  10. int(-pi//4)^(pi//4) (sec^2xdx)/(1+e^x)

    Text Solution

    |

  11. Evaluateint0^(1)((x-1)/(x+1))^(1/2)dx

    Text Solution

    |

  12. The value of (int0^n[x]dx)/(int0^n{x}dx is (where [x] and {x} denotes ...

    Text Solution

    |

  13. Evaluate: int0^(pi/2)(sinx+cosx)^2/(1+sin2x)^(1/2)dx

    Text Solution

    |

  14. Find the solution for x of the equation int(2^(1/2))^x1/(t(t^2-1)^(1/2...

    Text Solution

    |

  15. If I1= inte^(e^2)dx/logx and I2= int1^2e^x/xdx, then find relation bet...

    Text Solution

    |

  16. If int0^adx/(1+4x^2)= pi/8, then find the value of a.

    Text Solution

    |

  17. Evaluate int0^(pi/2)(cosx)/(1+sinx)^2dx

    Text Solution

    |

  18. Evaluate: int(pi/4)^((3pi)/4)dx/(1+cosx)

    Text Solution

    |

  19. int(-pi/3)^(pi/3) ((xsinx)dx)/(cos^2x) is

    Text Solution

    |

  20. The value of int(-3)^3(ax^5+bx^3+cx+k)dx where a,b, c, k are constant ...

    Text Solution

    |