Home
Class 12
MATHS
underset(xrarr(pi)/(4))(lim)(int(2)^(sec...

`underset(xrarr(pi)/(4))(lim)(int_(2)^(sec^(2)x)f(t)dt)/(x^(2-)(pi^(2))/(16))` is equal to

A

`(8)/(pi)f(2)`

B

`(2)/(pi)f(2)`

C

`(2)/(pi)f((1)/(2))`

D

4f(2)

Text Solution

Verified by Experts

The correct Answer is:
A
Using L' Hospital's rule, we have
`underset(x to pi//4)lim(overset(sec^(2)x)underset(2)intf(l)dt)/(x^(2)-(pi^(2))/(16))`
`=underset(x to pi//4)lim(2sec^(2)x tanx f(sec^(2)x))/(2x)=(2xx2xx1xxf(2))/(2xx(pi)/(4))=(8)/(pi)f(2)`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|145 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|12 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|87 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

lim_(xrarr(pi)/(4)) (int_(2)^(sec^(2)x)f(t)dt)/(x^(2-)(pi^(2))/(16)) is equal to

The value of lim _( x to (pi)/(4))(int_(2 ) ^(cosec ^(2)x)tg (t )dt)/(x ^(2)-(pi^(2))/(16)) is:

The value of lim _( x to (pi)/(4))(int_(2 ) ^(cosec ^(2)x)tg (t )dt)/(x ^(2)-(pi^(2))/(16)) is:

lim_(x to 0)(int_(-x)^(x) f(t)dt)/(int_(0)^(2x) f(t+4)dt) is equal to

lim_(xrarroo)((int_(0)^(x)e^(t^(2))dt)^(2))/(int_(0)^(x)e^(2t^(2))dt) is equal to

lim_(x to 0)(int_(0^(x) x e^(t^(2))dt)/(1+x-e^(x)) is equal to

lim_(x to oo)(int_0^(2x) te^(t^(2))dt)/(e^(4x^(2))) equals

lim(x->0)(1/(x^5)int_0^xe^(-t^2)dt-1/(x^4)+1/(3x^2)) is equal to

lim_(x to 0)(int_(0)^(x^(2))(tan^(-1)t)dt)/(int_(0)^(x^(2))sin sqrt(t)dt) is equal to :

The value of underset(xrarr(3pi)/(4))(lim)(1+root3(tanx))/(1-2cos^(2)x) is

OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Chapter Test 2
  1. underset(xrarr(pi)/(4))(lim)(int(2)^(sec^(2)x)f(t)dt)/(x^(2-)(pi^(2))/...

    Text Solution

    |

  2. The value of the integral int(0)^(2)x[x]dx

    Text Solution

    |

  3. The value of integral sum (k=1)^(n) int (0)^(1) f(k - 1+x) dx is

    Text Solution

    |

  4. Let f (x) be a function satisfying f(x)=f(x) with f(0) = 1 and g be th...

    Text Solution

    |

  5. If I=int(0)^(1)cos(2 cot^(-1)sqrt(((1-x)/(1+x))))dx then :

    Text Solution

    |

  6. The value of int(a)^(a+(pi//2))(sin^(4)x+cos^(4)x)dx is

    Text Solution

    |

  7. The vaue of int(-1)^(2) (|x|)/(x)dx is

    Text Solution

    |

  8. The value of int0^1 (x^(3))/(1+x^(8))dx is

    Text Solution

    |

  9. The value of int(0)^(3) xsqrt(1+x)dx, is

    Text Solution

    |

  10. Evaluate int(0)^(1)log(sin((pix)/(2)))dx

    Text Solution

    |

  11. Evaluate int(0)^(pi) xlog sinx dx

    Text Solution

    |

  12. If I(1)=int(0)^(oo) (dx)/(1+x^(4))dx and I(2)=underset(0)overset(oo)i...

    Text Solution

    |

  13. If f(x)={{:(x,xlt1),(x-1,xge1):}, then underset(0)overset(2)intx^(2)f(...

    Text Solution

    |

  14. The value of the integral overset(1)underset(0)int (1)/((1+x^(2))^(3//...

    Text Solution

    |

  15. Prove that: int0^(2a)f(x)dx=int0^(2a)f(2a-x)dxdot

    Text Solution

    |

  16. If int(0)^(36) (1)/(2x+9)dx =log k, is equal to

    Text Solution

    |

  17. The value of the integral int(0)^(pi//2) sin^(6) x dx, is

    Text Solution

    |

  18. If int(0)^(oo) e^(-x^(2))dx=sqrt((pi)/(2))"then"int(0)^(oo) e^(-ax^(2)...

    Text Solution

    |

  19. The value of the integral int 0^oo 1/(1+x^4)dx is

    Text Solution

    |

  20. The value of alpha in [0,2pi] which does not satify the equation int(p...

    Text Solution

    |

  21. lim(x to 0)(int(0)^(x^(2))sinsqrt(t) dt)/(x^(3)) is equl to

    Text Solution

    |