Home
Class 11
MATHS
If f(x) satisfies the condition of Rolle...

If `f(x)` satisfies the condition of Rolles theorem in [1, 2] then `int_1^2f^(prime)(x)dx` is equal to (A) 1 (B) 3 (C) 0 (D) none of these

A

3

B

0

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
It is givne that f(x) is continuous on [1,2] differentiable on (1,2) and f(2) =r(1)
`:.underset(1)overset(2)intf'(x)dx=[f(x)]_(1)^(2)=f(2)-f(1)=0`
Promotional Banner

Topper's Solved these Questions

  • MEAN VALUE THEOREMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|4 Videos

  • MEAN VALUE THEOREMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|28 Videos

  • MEAN VALUE THEOREMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|28 Videos

  • MATRICES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • PAIR OF STRAIGHT LINES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|18 Videos

Similar Questions

Explore conceptually related problems

If f(x) satisfies the condition of Rolle's theorem in [1,2] , then int_1^2 f'(x) dx is equal to (a) 1 (b) 3 (c) 0 (d) none of these

If f(x) satisfies the condition of Rolle's theorem in [1,2] , then int_1^2 f'(x) dx is equal to (a) 1 (b) 3 (c) 0 (d) none of these

If y=f(x) satisfies has conditions of Rolle's theorem in [2, 6], then int_(2)^(6)f'(x)dx is equal to

If f(x) satisfies the condition for Rolle's heorem on [3,5] then int_(3)^(5) f(x) dx equals

int_0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) pi (D) none of these"

Let f(x)=max. {2-x,2,1+x} then int_(-1)^1 f(x)dx= (A) 0 (B) 2 (C) 9/2 (D) none of these

If f(x) satisfies the requirements of Rolle's Theorem in [1,2] and f(x) is continuous in [1,2] then int_(1)^(2) f'(x) dx is equal to

If f(x)=int_0^1(dt)/(1+|x-t|) ,then f^(prime)(1/2) is equal to (a)0 (b) 1/2 (c) 1 (d) none of these

Let f(x) be a function satisfying f\'(x)=f(x) with f(0)=1 and g(x) be the function satisfying f(x)+g(x)=x^2 . Then the value of integral int_0^1 f(x)g(x)dx is equal to (A) (e-2)/4 (B) (e-3)/2 (C) (e-4)/2 (D) none of these

The function f(x)=x(x+3)e^(-(1/2)x) satisfies the conditions of Rolle's theorem in (-3,0). The value of c, is

OBJECTIVE RD SHARMA ENGLISH-MEAN VALUE THEOREMS-Section I - Solved Mcqs
  1. If 27a+9b+3c+d=0 then the equation 4ax^(3)+3bx^(2)+2cx+d has at leat ...

    Text Solution

    |

  2. Which of the following is/are correct? Between any two roots of e^xcos...

    Text Solution

    |

  3. If the functions f(x) and g(x) are continuous on [a,b] and differenti...

    Text Solution

    |

  4. Let f be a function which is continuous and differentiable for all rea...

    Text Solution

    |

  5. The value of C ( if exists ) in Lagrange's theorem for the function |x...

    Text Solution

    |

  6. The equation sin x + x cos x = 0 has at least one root in

    Text Solution

    |

  7. Let f(x)=ax^(5)+bx^(4)+cx^(3)+dx^(2)+ ex, where a,b,c,d,e in R and f(x...

    Text Solution

    |

  8. If f''(x) le0 "for all" x in (a,b) then f'(x)=0

    Text Solution

    |

  9. In [0, 1] Lagrange's mean value theorem is not applicable to

    Text Solution

    |

  10. It is given that the Rolles theorem holds for the function f(x)=x^3...

    Text Solution

    |

  11. Let (x) satisfy the required of Largrange's Meahn value theorem in [0...

    Text Solution

    |

  12. If f(x) satisfies the condition of Rolles theorem in [1, 2] then int1^...

    Text Solution

    |

  13. If the function f(x)= x^(3)-6x^(2)+ax+b satisfies Rolle's theorem in t...

    Text Solution

    |

  14. If f(x)=x^(alpha)log x and f(0)=0, then the value of 'alpha' for which...

    Text Solution

    |

  15. A value of C for which the coclusion of mean value theorem holds for t...

    Text Solution

    |

  16. For a twice differentiable function f(x),g(x) is defined as g(x)=f^(pr...

    Text Solution

    |

  17. Let f be two differentiable function satisfying f(1)=1,f(2)=4, f(3)=9,...

    Text Solution

    |

  18. Let f:[0,4] in R be acontinuous function such that |f(x)|le2 "for all"...

    Text Solution

    |

  19. If f(x)=(x-p)(x-q)(x-r) where plt qlt ltr, are real numbers, then the ...

    Text Solution

    |

  20. Let f,g:[-1,2]vecR be continuous functions which are twice differentia...

    Text Solution

    |