Home
Class 12
MATHS
Ifint(sinx)^1t^2f(t)dt=1-sinx ,w h e r e...

`Ifint_(sinx)^1t^2f(t)dt=1-sinx ,w h e r e .x in (0,pi/2),` then find the value of `f(1/(sqrt(3)))dot`

A

3

B

`sqrt(3)`

C

`(1)/(3)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have, `overset(1)underset(ainx)int t^(2)f(t)dt=1-sin x`
`rArr (d)/(dx)(overset(1)underset(sinx)int t^(2)f(t)dt)=-cos`
`0-cos x sin^(2)x f(sin x)=-cos x` [Using Leibnitz's rule]
`rArr f(sin x)=(1)/(sin^(2)x)rArrf((1)/(sqrt(3)))=3`
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

If int_(sinx)^(1)t^(2) (f(t)) dt = (1-sinx) , then f ((1)/(sqrt(3))) is

f(x)=int_1^x(tan^(-1)(t))/t dt \ AAx in R^+, then find the value of f(e^2)-f(1/(e^2))

If f(x)=1+1/x int_1^x f(t) dt, then the value of f(e^-1) is

For x >0,l e tf(x)=int_1^x(logt)/(1+t)dtdot Find the function f(x)+f(1/x) and find the value of f(e)+f(1/e)dot

For x >0,l e tf(x)=int_1^x(logt)/(1+t)dtdot Find the function f(x)+f(1/x) and find the value of f(e)+f(1/e)dot

Let x in (0,pi/2)dot Then find the domain of the function f(x)=1/sqrt((-(log)_(sinx)tanx))

If lim_(trarrx)(e^(t)f(x)-e^(x)f(t))/((t-x)(f(x))^(2))=2 andf(0)=(1)/(2), then find the value of f'(0).

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.

If lim_(trarrx) (e^(t)f(x)-e^(x)f(t))/((t-x)(f(x))^(2))=2 andf(0)=(1)/(2), then find the value of f'(0).

If y=1/(t^2+t-2),w h e r et=1/(x-1), then find the number of points where f(x) is discontinuous.

OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Chapter Test 2
  1. Ifint(sinx)^1t^2f(t)dt=1-sinx ,w h e r e .x in (0,pi/2), then find th...

    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

    |