Home
Class 12
MATHS
If f(x) satisfies the condition of Rolle...

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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • JEE MAIN

    JEE MAINS PREVIOUS YEAR ENGLISH|Exercise MATH|21 Videos

  • LIMITS AND DERIVATIVES

    JEE MAINS PREVIOUS YEAR ENGLISH|Exercise All Questions|5 Videos

Similar Questions

Explore conceptually related problems

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

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 2f(x)-3f(1/x)=x^2(x!=0), then f(2) is equal to (a) -7/4("b")""5/2 (c) -1 (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

f(x) is a continuous function for all real values of x and satisfies int_n^(n+1)f(x)dx=(n^2)/2AAn in Idot Then int_(-3)^5f(|x|)dx is equal to (a) (19)/2 (b) (35)/2 (c) (17)/2 (d) none of these

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

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"

If f(x)=(x+1)^(cotx) be continuous at x=0, the f(0) is equal to (a) 0 (b) 1/e (c) e (d) none of these

f(x) is a continuous function for all real values of x and satisfies int_n^(n+1)f(x)dx=(n^2)/2AAn in Idot Then int_(-3)^5f(|x|)dx is equal to (19)/2 (b) (35)/2 (c) (17)/2 (d) none of these

JEE MAINS PREVIOUS YEAR ENGLISH-JEE MAINS-All Questions
  1. From a group of 10 persons consisting of 5 lawyers, 3 doctors and 2 ...

    Text Solution

    |

  2. A die is thrown a fixed number of times. If probability of getting eve...

    Text Solution

    |

  3. If f(x) satisfies the condition of Rolle's theorem in [1,2], then int1...

    Text Solution

    |

  4. The antiderivative of (2^x)/(sqrt(1-4^x)) w.r.t x is (A) (log)2edotsin...

    Text Solution

    |

  5. The minimum value of, 25cosec^2x+16sin^2x is (A) 41 (B) 42 (C) 43 ...

    Text Solution

    |

  6. if the graph of the cont. function y=f(x) passes through the point (a,...

    Text Solution

    |

  7. The sum of the intercepts made by the plane a x+b y+c z=d on the three...

    Text Solution

    |

  8. The value of sin^(-1)("cos"(cos^(-1)(cosx)+sin^(-1)(sinx))), where x i...

    Text Solution

    |

  9. If sin^(-1)x-cos^(-1)x=pi/6 , then x= (a)1/2 (b) (sqrt(3))/2 (c) -1/2...

    Text Solution

    |

  10. Area bounded by the curve y=sqrt(sin[x]+[sinx]),(w h e r e[dot] is gre...

    Text Solution

    |

  11. Let f:[0,r]vec[-1,5],w h e r ef(x)={x^2-1,0lt=x<2 4,x=2,t h e nf(x)i s...

    Text Solution

    |

  12. If a triangle is inscribed in a rectangular hyperbola, it’s orhtocente...

    Text Solution

    |

  13. A box contains 5 different res and 6, different whit balls. In how man...

    Text Solution

    |

  14. Let y=g(x) be the solution of the differential equation sinx ((dy)/(...

    Text Solution

    |

  15. The sum of the co-efficients of all odd degree terms in the expansion ...

    Text Solution

    |

  16. Let S={t in R: f(x)=|x-pi|(e^(|x|)-1)sin|x| is not differentiable at t...

    Text Solution

    |

  17. about to only mathematics

    Text Solution

    |

  18. If the curves y^2=6x, 9x^2+by^2=16 intersect each other at right angle...

    Text Solution

    |

  19. A straight line through a fixed point (2,3) intersects the coordinate ...

    Text Solution

    |

  20. Tangent and normal are drawn at P(16,16) on the parabola y^2=16x which...

    Text Solution

    |