Home
Class 12
MATHS
If f(x) is a continuous function AAx in ...

If `f(x)` is a continuous function `AAx in R ,` then which of the following is (are) true, (a)`int_4^(16)f(sqrt(x))dx=4cf(c)` for some `c in (2,4)` (b)`int_4^(16)f(sqrt(x))dx=4cf(c)` for some `c in (2,16)` (c)`int_4^(16)f(sqrt(x))dx=6(2-cf^(prime)(c))` for some `c in (4,16),` if `f(2)=f(4)` (d)`int_4^(16)f(sqrt(x))dx=6(2-cf^(prime)(c))` for some `c in (2,4),` if `f(2)=f(4)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos
  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

"F i n d"int_4^9sqrt(x)dx

If f(x) is continuous and int_(0)^(9)f(x)dx=4 , then the value of the integral int_(0)^(3)x.f(x^(2))dx is

Which of the following is incorrect? int_(a+ c)^(b+c)f(x)dx=int_a^bf(x+c)dx int_(ac)^(b c)f(x)dx=cint_a^bf(c x)dx int_(-a)^af(x)dx=1/2int_(-a)^a(f(x)+f(-x)dx None of these

Let f(x) be a continuous function in R such that f(x)+f(y)=f(x+y) , then int_-2^2 f(x)dx= (A) 2int_0^2 f(x)dx (B) 0 (C) 2f(2) (D) none of these

If int(1)/(x^(2)+2x+2)dx=f (x) +C , then f (x)=

Let f be a continuous function on [a , b]dot If F(x)=(int_a^xf(t)dt-int_x^bf(t)dt)(2x-(a+b)), then prove that there exist some c in (a , b) such that int_a^cf(t)dt-int_c^bf(t)dt=f(c)(a+b-2c)dot

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in Rdot If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to (a)6 (b) 0 (c) 3f(3) (d) 2f(0)

If int (2^(x))/(sqrt(1-4^(x))) dx = k sin ^(-1) (f(x)) + C then :

Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in [0,a] . Then int_0^a dx/(1+e^(f(x)))= (A) a (B) a/2 (C) 1/2f(a) (D) none of these

If f(x)=(x-4)/(2sqrt(x)) , then f^(prime)(1) is a. 5/4 b. 4/5 c. 1 d. 0

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. A point z moves on the curve |z-4-3i| =2 in an argand plane. The maxim...

    Text Solution

    |

  2. If alpha, beta and gamma are the roots of the equation x^(3)-px^(2)+qx...

    Text Solution

    |

  3. If f(x) is a continuous function AAx in R , then which of the followi...

    Text Solution

    |

  4. Statement 1: If|x+3|+5=|x+8|t h e nxgeq-3 Statement 2: |a|+|b|=|a+b...

    Text Solution

    |

  5. Let In=int- 1^1|x|(1+x+(x^2)/2+(x^3)/3+.....+(x^(2n))/(2n))dx where ...

    Text Solution

    |

  6. If sintheta=5sin(theta+varphi),t h e ntan(theta+varphi)= (sinvarphi)/...

    Text Solution

    |

  7. If the range of the integral I=int0^(1/2)(dx)/(sqrt(1-x^(2n))) for nge...

    Text Solution

    |

  8. Three friends whose ages form a G.P. divide a certain sum of money in ...

    Text Solution

    |

  9. A straight line moves such that the algebraic sum of the perpendicular...

    Text Solution

    |

  10. In how many ways 10 passengers can board three buses if no bus remains...

    Text Solution

    |

  11. sinx+cosx=y^2-y+a has no value of x for any value of y if a belongs to...

    Text Solution

    |

  12. Let f (x) be a polynomial of degree 5 with leading coefficient unity s...

    Text Solution

    |

  13. "I f"f(x)={x^3-6x^2; ifxi sr a t ion a l-11 x+6;ifxi si r r a t ion a ...

    Text Solution

    |

  14. If the equation of plane containing the line x-y+z=0a n dx+y+z-2=0 and...

    Text Solution

    |

  15. The number of values of a for which equations x^3+a x+1=0 and x^4+a x^...

    Text Solution

    |

  16. If the equation of plane containing the line x-y+z=0a n dx+y+z-2=0 and...

    Text Solution

    |

  17. Let f(x)=ax^(2)+bx+c, g(x)=ax^(2)+px+q, where a, b, c, q, p in R and b...

    Text Solution

    |

  18. If the equation of plane containing the line x-y+z=0a n dx+y+z-2=0 and...

    Text Solution

    |

  19. If a=(25-x^2)/(16) and (loga) ((24-2x-x^2))/(14)gt1 ,then x in

    Text Solution

    |

  20. If the equation of plane containing the line x-y+z=0a n dx+y+z-2=0 and...

    Text Solution

    |