Home
Class 12
MATHS
Let F : R to R be a thrice differentia...

Let F : R `to` R be a thrice differentiable function . Suppose that `F(1)=0,F(3)=-4 and F(x) lt 0 ` for all `x in (1,3)`. `f(x) = x F(x)` for all `x inR`.
If `int_(1)^(3)x^(2)F'(x)dx=-12 andint_(1)^(3)x^(3)F'' (x)dx =40`, then the correct expression (s) is //are

A

`9f'(3)+f'(1)-32=0`

B

`int_(1)^(2)f(x)dx=12`

C

`9f'(3)-f'(1)+32=0`

D

`int_(1)^(3)f(x)dx=-12`

Text Solution

Verified by Experts

The correct Answer is:
C, D
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE main (Archive)|51 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|81 Videos

Similar Questions

Explore conceptually related problems

Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3)=-4 and F'(x)lt0 for all x epsilon(1//2,3) . Let f(x)=xF(x) for all x inR . Then the correct statement(s) is (are)

Let f be a differentiable function such that f(1) = 2 and f'(x) = f (x) for all x in R . If h(x)=f(f(x)), then h'(1) is equal to

Let f:R to R and g:R to R be differentiable functions such that f(x)=x^(3)+3x+2, g(f(x))=x"for all "x in R , Then, g'(2)=

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then f(x) is

If f:R->R is a twice differentiable function such that f''(x) > 0 for all x in R, and f(1/2)=1/2 and f(1)=1, then

The number of continous and derivable function(s) f(x) such that f(1) = -1 , f(4) = 7 and f'(x) gt 3 for all x in R is are :

The number of continous and derivable function(s) f(x) such that f(1) = -1 , f(4) = 7 and f'(x) gt 3 for all x in R is are :

Let f be a differentiable function such that f'(x) = f(x) + int_(0)^(2) f(x) dx and f(0) = (4-e^(2))/(3) . Find f(x) .

Let f[1, infty) to [2, infty) be a differentiable function such that f(1) =1/3 . If 6 int_(1)^(x) f(t) dt = 3x f(x) -x^(3) for all x ge 1 , then the value of 3f(2) is

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-JEE Advanced (Archive)
  1. Let f:[a,b]to[1,oo) be a continuous function and let g:RtoR be defined...

    Text Solution

    |

  2. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

  3. Let F : R to R be a thrice differentiable function . Suppose that F(...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. Let fandg be real valued functions defined on interval (-1,1) such tha...

    Text Solution

    |

  7. Let alpha,betainR be such that underset(xto0)lim(x^(2)sin(betax))/(alp...

    Text Solution

    |

  8. If f(x) is a polynomial of degree 4 having extremum at x=1,2 and lim(x...

    Text Solution

    |

  9. Let f:[1,oo] be a differentiable function such that f(1)=2. If int1...

    Text Solution

    |

  10. The largest value of the non-negative integer a for which lim(xto1) ...

    Text Solution

    |

  11. Let f: R to R and g:R to R be respectively given by f(x) =|x|+1 and g...

    Text Solution

    |

  12. Let f(x) = x+ log(e)x-xlog(e)x,x in (0,oo) List I contains informati...

    Text Solution

    |

  13. Let f(x) = x+ log(e)x-xlog(e)x,x in (0,oo) List I contains informati...

    Text Solution

    |

  14. Let f(x) = x+ log(e)x-xlog(e)x,x in (0,oo) List I contains informati...

    Text Solution

    |

  15. Match the Columns:

    Text Solution

    |

  16. Match the Columns:

    Text Solution

    |

  17. If f(x)={(x/(1+e^(1//x)),x!=0),(0,x=0):} then at x=0

    Text Solution

    |

  18. If f(r)(x), g(r)(x), h(r) (x), r=1, 2, 3 are polynomials in x such th...

    Text Solution

    |

  19. Find the derivative of sec^(-1)((1)/(2x^(2)-1))" w.r.t. "sqrt(1-x^(2))...

    Text Solution

    |

  20. ABC is an isosceles triangle inscribed in a circle of radius rdot If A...

    Text Solution

    |