Home
Class 12
MATHS
1Let f be a differentiable function defi...

1Let `f` be a differentiable function defined on `[0,(pi)/(2)]` such that `f(x)>0` and `f(x)+int_(0)^(x)f(t)sqrt(1-(log_(e)f(t))^(2))dt=e,AA x in[0,pi x in[0,pi]` .Then `(6 log_e f(pi/6))^2` is equal to

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • JEE MAINS 2022

    JEE MAINS PREVIOUS YEAR|Exercise MATHEMATICS (SECTION - B)|10 Videos

  • LIMITS AND DERIVATIVES

    JEE MAINS PREVIOUS YEAR|Exercise All Questions|14 Videos

Similar Questions

Explore conceptually related problems

Let f(x) be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt then int_(0)^(1)f(x)dx=

Let f be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt then prove that f(x)=(x^(3))/(3)+x^(2)

If a differentiable function f(x) satisfies f(x)=int_(0)^(x)(f(t)cos t-cos(t-x))dt then value of (1)/(e)(f''((pi)/(2))) is

if f be a differentiable function such that f(x) =x^(2)int_(0)^(x)e^(-t)f(x-t). dt. Then f(x) =

Let f:R rarr R be a differentiable and strictly decreasing function such that f(0)=1 and f(1)=0. For x in R, let F(x)=int_(0)^(x)(t-2)f(t)dt

If int_(0)^(x)f(t)dt=e^(x)-ae^(2x)int_(0)^(1)f(t)e^(-t)dt , then

The derivative of f(x)=int_(x^(2))^(x^(3))(1)/(log_(e)(t))dt,(x>0), is

if f(x) is a differential function such that f(x)=int_(0)^(x)(1+2xf(t))dt&f(1)=e , then Q. int_(0)^(1)f(x)dx=

F(x)= int_(0)^(x)(cost)/((1+t^(2)))dt0lt=xlt=2pi . Then

If int_(e)^(x) t f(t)dt=sin x-x cos x-(x^(2))/(2) for all x in R-{0} , then the value of f((pi)/(6)) will be equal to

JEE MAINS PREVIOUS YEAR-JEE MAINS 2023 JAN ACTUAL PAPER-Question
  1. int((3sqrt2)/4)^((3sqrt(3))/(4)) (48)/(sqrt(9-4x^(2)))dx is equal to

    Text Solution

    |

  2. The value of ((1+sin((2 pi)/(9))+i cos((2 pi)/(9))))/(1+sin((2 pi)/(9)...

    Text Solution

    |

  3. 1Let f be a differentiable function defined on [0,(pi)/(2)] such that ...

    Text Solution

    |

  4. If (1^(3)+2^(3)+3^(3)+... "upto n terms")/(1*3+2*5+3*7+... "upto n ter...

    Text Solution

    |

  5. The equations of the sides AB,BC and CA of a triangle ABC are :2x+y=0,...

    Text Solution

    |

  6. Three ums A,B and C contain + red, 6 black. 5 black and lambda red, 4 ...

    Text Solution

    |

  7. The minimum aumber of elements that must be added to the relation R={(...

    Text Solution

    |

  8. Let vec a=hat i+2hat j+lambdahat k,vec b=3hat i-5hat j-2hat k,vec a*ve...

    Text Solution

    |

  9. Let the sum of the coefficients of the first three terms in the expans...

    Text Solution

    |

  10. If the area of the region bounded by the curves y^(2)-2y=-x,x+y=0 is A...

    Text Solution

    |

  11. 9If the shortest between the lines (x+sqrt(6))/(2)=(y-sqrt(6))/(3)=(z-...

    Text Solution

    |

  12. Let S={theta in[0,2 pi):tan(pi cos theta)+tan(pi sin theta)=0}. Then s...

    Text Solution

    |

  13. Let y = y(x) be the solution of the differential equation x^3dy + (xy ...

    Text Solution

    |

  14. The area enclosed by the curves y^2+ 4x = 4 and y – 2x = 2 is:

    Text Solution

    |

  15. Let Ω be the sample space and A ⊆ Ω be an event.Given below are two st...

    Text Solution

    |

  16. The value of sum(r=0)^22 "^(22)Cr "^23Cr is

    Text Solution

    |

  17. Let alpha be a root of the equation (a – c) x^2 + (b – a) x + (c – b) ...

    Text Solution

    |

  18. lim(trarr0)(1^(1/sin^2t)+2^(1/sin^2t)+..n^(1/sin^2t))^(sin^2t)

    Text Solution

    |

  19. The distance of the point (–1, 9,–16) from the plane 2x + 3y – z = 5 m...

    Text Solution

    |

  20. Let N denote the number that turns up then a fair die is rolled. If th...

    Text Solution

    |