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

`lim_(x to 0)(int_(0)^(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 ENGLISH|Exercise Chapter Test 1|57 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_(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 to 0)int_(0)^(x^(2)){(sinsqrt(t)) (tansqrt(t))dt}/(x^(4))

Given that lim_(x to 0)(int_(0)^(x)(t^(2))/(sqrt(a+t))dt)/(bx-sinx) = 1 , then find the values of a and b.

Let L_(1) = lim_(xrarr0^(+)) (int_(0)^(x^(2)) sinsqrt(t)dt)/(x-sinx) , then identify the correct option(s).

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

lim_(xto oo) (int_(0)^(x)tan^(-1)t\ dt)/(sqrt(x^(2)+1)) is equal to

underset(xto0)("lim")(int_(0)^(x)t tan (5t)dt)/x^3 is equal to :

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

Evaluate lim_(xto0)(x-(int_(0)^(x)costdt))/(x^(3)-6x)

OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Chapter Test 2
  1. The value of the integral int 0^oo 1/(1+x^4)dx is

    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)^(x^(2))sinsqrt(t) dt)/(x^(3)) is equl to

    Text Solution

    |

  4. If [int0^1(dt)/(t^2+2tcosalpha+1)]x^2-[int- 3^3(t^2sin2t)/(t^2+1)dt]x-...

    Text Solution

    |

  5. The number of value of alpha in the interval [-pi,0] satisfying sin...

    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 int0^pi1/(5+3cosx)dx is a. pi//2 b. pi//4 c. 0 d. pi...

    Text Solution

    |

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

    Text Solution

    |

  9. underset(nrarr0)" lim" underset(r=1)overset(n)sum((r^(3))/(r^(4)+n^(4)...

    Text Solution

    |

  10. The value of lim(n to oo) {(1+(1)/(n))(1+(2)/(n))(1+(3)/(n))...(2)}^(1...

    Text Solution

    |

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

    Text Solution

    |

  12. If I(n)=int(0)^(pi//4) tan^(n)x dx, (ngt1 is an integer ), then (a) I(...

    Text Solution

    |

  13. If Im=int1^x(logx)^mdx satisfies the relation (Im)=k-l I(m-1) then

    Text Solution

    |

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

    Text Solution

    |

  15. If I(mn)=int(0)^(1)x^(m-1)(1-x)^(n-1)dx,(m, n epsilon I, m,n ge 0 ), t...

    Text Solution

    |

  16. Find the points of maxima /minima of int(0)^(x^(2))(t^(2)-5t+4)/(2+e^(...

    Text Solution

    |

  17. Evaluate the following definite integral: int(-pi)^(pi)(2x(1+sinx))/(1...

    Text Solution

    |

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

    Text Solution

    |

  19. The value of the integral int(alpha)^(beta) sqrt((x-alpha)(beta-x))dx,...

    Text Solution

    |

  20. If int(0)^(x^(2)) sqrt(1+t^(2)) dt, then f'(x)n equals

    Text Solution

    |