Home
Class 12
MATHS
let f be a continuous function satisfyin...

let `f` be a continuous function satisfying `int_0^(t^2) 9f(x)+x^2)dx=(4t^3)/3, AA tgt0`. Then `f(pi^2/4)` is equal to

A

`pi^2(1-pi^2/16)`

B

`-pi(1+pi^3/16)`

C

`pi(1-pi^3/16)`

D

`-pi^2(1+pi^2/16)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • JEE MAIN 2022

    JEE MAINS PREVIOUS YEAR|Exercise Question|454 Videos
  • JEE MAIN 2024

    JEE MAINS PREVIOUS YEAR|Exercise Questions|18 Videos

Similar Questions

Explore conceptually related problems

Let f(x) be a differentiable function such that int_(t)^(t^(2))xf(x)dx=(4)/(3)t^(3)-(4t)/(3)AA t ge0 , then f(1) is equal to

If a continuous function f satisfies int_(0)^(f(x))t^(3)dt=x^(2)(1+x) for all x>=0 then f(2)

Let f: R to R be a continuous function. Then lim_(x to pi//4) (pi/4 int_2^(sec^2x) f(x)dx)/(x^2 - pi^2/16) is equal to :

Let f: R to R be a continuous function. Then lim_(x to pi//4) (pi/4 int_2^(sec^2x) f(x)dx)/(x^2 - pi^2/16) is equal to :

If f is continuous function and F(x)=int_(0)^(x)((2t+3)*int_(t)^(2)f(u)du)dt, then |(F^(n)(2))/(f(2))| is equal to

Let f(x) be a function satisfying f'(x) = f(x) and f(0) = 2. Then int(f(x))/(3+4f(x))dx is equal to

Let f be a continuous function satisfying the equation int_(0)^(x)f(t)dt+int_(0)^(x)tf(x-t)dt=e^(-x)-1 , then find the value of e^(9)f(9) is equal to…………………..

JEE MAINS PREVIOUS YEAR-JEE MAIN 2023-Question
  1. Eight persons are to be transported from city A to city B in three car...

    Text Solution

    |

  2. Let veca=2hati=7hatj-hatk,vecb=3hati+5hatk and vec c=hati-hatj=2hatk. ...

    Text Solution

    |

  3. let f be a continuous function satisfying int0^(t^2) 9f(x)+x^2)dx=(4t^...

    Text Solution

    |

  4. For alpha,beta,gamma,delta in NN, if int((x/e)^(2x)+(e/x)^(2x))logx dx...

    Text Solution

    |

  5. Let g(x)=f(x)+f(1-x) and f''(x) gt 0,x in (0,1). If g is decreasing in...

    Text Solution

    |

  6. The statement ~[pvv(~(p^^q))] is equivalent to

    Text Solution

    |

  7. Let a circle of radius of 4 be concentric to the ellipse 15x^2+19y^2=2...

    Text Solution

    |

  8. Let S={x in (-pi/2,pi/2) : 9^(1-tan^2x)+9^(tan^2x)=10} and beta=sum(x ...

    Text Solution

    |

  9. Let A={2,3,4} and B={8,9,12}. Then the number of elements in the relat...

    Text Solution

    |

  10. Let a die be rolled n times. Let the probability of getting odd number...

    Text Solution

    |

  11. Let S={z=x=iy: (2z-3i)/(4z+2i) is a real number}. Then which of the fo...

    Text Solution

    |

  12. If Sn=4+11+21+34+50+... to n terms, then 1/60(S(29)-S9) is equal to

    Text Solution

    |

  13. If A=1/(5!6!7!)[[5!,6!,7!],[6!,7!,8!],[7!,8!,9!]], then |adj(adj(2A))|...

    Text Solution

    |

  14. Let A be the point (1,2) and B be any point on the curve x^2+y^2=16. I...

    Text Solution

    |

  15. If the coefficients of x and x^2 in (1+x)^p(1-x)^q are 4 and -5 respec...

    Text Solution

    |

  16. If the points P and Q are respectively the circumcenter and the orthoc...

    Text Solution

    |

  17. Let the line x/1=(6-y)/2=(z+8)/5 intersect the lines (x-5)/4=(y-7)/3=(...

    Text Solution

    |

  18. Suppose a1, a2, 2, a3,a4 be in an arithmeticogeometric progression. If...

    Text Solution

    |

  19. In the figure theta1+theta2=pi/2 and sqrt3(BE)=4(AB). If the area of t...

    Text Solution

    |

  20. If the area of the region {(x, y) : |x^2 – 2| le y lex} is A then 6A +...

    Text Solution

    |