Home
Class 12
MATHS
Let I (a) =int(0)^(pi) ((x)/(a)+ a sin x...

Let `I (a) =int_(0)^(pi) ((x)/(a)+ a sin x)^(2) dx`, where 'a' is positive real .
The value of 'a' for which I(a) attains its minimum value, is

A

`sqrt(pisqrt((2)/(3)))`

B

`sqrt(pisqrt((3)/(2)))`

C

`sqrt((pi)/(16))`

D

`sqrt((pi)/(13))`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|10 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|17 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 6|10 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

Let I=int_(0)^((pi)/(2))((sin x)/(x))dx, then

Let I_(n)=int_(0)^(pi//2) sin^(n)x dx, nin N . Then

Let I=int_(0)^(2pi)(xsin^(8)x)/(sin^(8)x+cos^(8)x)dx , then I is equal to :

The value of int_(0)^(pi) x sin^(3) x dx is

I=int_(0)^(2 pi)e^(sin^(2)x+sin x+1)dx then

The value of int_(0)^(2pi)[sin2x(1+cos3x)] dx, where [t] denotes

If I=int_(0)^(2pi) sin^(2) x" dx" , then

Evaluate : I = int_(0)^(2 pi)(sin x)dx =

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Single Option Correct Type Questions)
  1. For f(x) =x^(4) +|x|, let I(1)= int (0)^(pi)f(cos x) dx and I(2)= int(...

    Text Solution

    |

  2. Let f be a positive function. If I1 = int(1-k)^k x f[x(1-x)]\ dx and I...

    Text Solution

    |

  3. Suppose that the quadratic function f(x) = ax^(2) + bx +c is non-negat...

    Text Solution

    |

  4. Let I (a) =int(0)^(pi) ((x)/(a)+ a sin x)^(2) dx, where 'a' is positiv...

    Text Solution

    |

  5. The set of value of 'a' which satisfy the equation int0^2(t-log2a)dt...

    Text Solution

    |

  6. lim(x rarr infty) (x^(3) int(-1//x)^(1//x)("In" (1+t^(2)))/(1+e^(t)) d...

    Text Solution

    |

  7. The value of sqrt(pi(int(0)^(2008)x| sinpi x| dx)) is equal to

    Text Solution

    |

  8. lim(n rarr infty) sum(k=1)^(n) (n)/(n^(2)+k^(2)x^(2)),x gt 0 is equa...

    Text Solution

    |

  9. Let a gt 0 and f(x) is monotonic increase such that f(0)=0 and f(a)=b...

    Text Solution

    |

  10. int(-1/sqrt3)^(-1/sqrt3)(x^4)/(1-x^4)cos^(- 1)((2x)/(1+x^2))dx

    Text Solution

    |

  11. int(0)^(infty)f(x+(1)/(x)). (In x )/(x)dx is equal to

    Text Solution

    |

  12. lim(lamda to 0)(int(0)^(1) (1+x)^(lambda ) dx)^(1//lambda) Is equal t...

    Text Solution

    |

  13. If g(x) is the inverse of f(x) and f(x) has domain x in [1,5], where...

    Text Solution

    |

  14. The value of the definite integral int(0)^(pi//2)sin x sin 2x sin 3x d...

    Text Solution

    |

  15. If f(x)= int(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable functi...

    Text Solution

    |

  16. The number of integral solutions of the equation 4int (0)^( infty)(In"...

    Text Solution

    |

  17. int(0)^(16n^(2)//pi) "cos" (pi)/(2)[(xpi)/(n)] dx is equal to

    Text Solution

    |

  18. If int-2^-1 (ax^2-5)dx=0 and 5 + int1^2 (bx + c) dx = 0, then

    Text Solution

    |

  19. The value of int(3)^(6)(sqrt(x+sqrt(12x-36))+sqrt(x-sqrt(12x- 36)))dx...

    Text Solution

    |

  20. Let In=int(-n)^n({x+1}*{x^2+2}+{x^2+2}{x^3+4})dx, where {*} denotet th...

    Text Solution

    |