Home
Class 12
MATHS
lim(x to 0)(int(0)^t(x^(2))sinsqrt(t) dt...

`lim_(x to 0)(int_(0)^t(x^(2))sinsqrt(t) dt)/(x^(3))` is equl to

A

`1//3`

B

1

C

`2//3`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Chapter Test 1|60 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA|Exercise Exercise|86 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

lim_(x rarr 0) (int_(0)^(x) t tan(5t)dt)/(x^(3)) is equal to :

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

Evaluate :lim_(x rarr0)(int_(0)^(x^(2))sin sqrt(t)dt)/(x^(3))

The value of lim_( x to 0) (int_(0)^(x) sin t^(2) dt) / x^(2) is

The value of lim_(x rarr0)(int_(0)^(x) xe^(t^(2))dt)/(1+x-e^(x)) is equal to

The value of (lim_(x rarr0)(1)/(x^(6))int_(0)^(x^(2))sin(t^(2))dt) is equal to

OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Chapter Test 2
  1. If int(pi//2)^(x) sqrt(3-2sin^(2)u) dx+int(dx)^(dy) equal pi//2

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. If x satisfies the equation x^(2)( int(0)^(1) (dt)/(t^(2)+ 2t cos al...

    Text Solution

    |

  5. The value of alpha in (-pi, 0) satisfying sin alpha+int(alpha)^(2alpha...

    Text Solution

    |

  6. The value of int(0)^(pi//2) (sin^(3)x cos x)/(sin^(4)x+ cos^(4)x )dx i...

    Text Solution

    |

  7. The value of int(0)^(pi) (1)/(5+3cosx)dx, is

    Text Solution

    |

  8. underset(nrarroo)"lim"[sin'(pi)/(n)+sin'(2pi)/(n)+"......"+sin'((n-1))...

    Text Solution

    |

  9. lim(n to oo) sum(r=1)^(n) {(r^(3))/(r^(4)+n^(4))} equals

    Text Solution

    |

  10. lim(n-gtoo)[(1+1/n)(1+2/n)(1+n/n)]^(1/n)

    Text Solution

    |

  11. Evaluate: (lim)(nvecoo)n[1/(n a)+1/(n a+1)+1/(n a+2)++1/(n b)]

    Text Solution

    |

  12. The solution of the equation int(0)^(x) (1)/(xsqrt(2^(2)-1))dx=(pi)/(1...

    Text Solution

    |

  13. Let I(n)=int(0)^(pi//4) tan^(n) x dx, (n gt1 and n in N), then

    Text Solution

    |

  14. If I(m)=int(1)^(x) (log x)^(m)dx satisfies the relation Im = k-lI(m-1...

    Text Solution

    |

  15. If I(m)=int(0)^(oo) e^(-x)x^(n-1)dx, "then" int(0)^(oo) e^(-lambdax) x...

    Text Solution

    |

  16. If I(m,n)=int(0)^(1)x^(m-1) (1-x)^(n-1)dx then

    Text Solution

    |

  17. The total number of extremum(s) of y=int0^(x^2)(t^2-5t+4)/(2+e^t)dt ar...

    Text Solution

    |

  18. The tangent to the curve y=f (x) at the point with abscissa x =1 from ...

    Text Solution

    |

  19. int(-pi)^(pi) (2x(1+ sinx))/(1+ cos^(2))dx is

    Text Solution

    |

  20. The value of the inntegral int(alpha)^(beta) (1)/(sqrt((x-alpha)(beta-...

    Text Solution

    |