Home
Class 12
MATHS
Let f (x) =x ^(2) +2x -t ^(2) and f(x)=0...

Let `f (x) =x ^(2) +2x -t ^(2) and f(x)=0` has two root `alpha (t ) and beta (t) (alpha lt beta)` where t is a real parameter. Let `I (t)=int _(alpha ) ^(beta)f (x)` dx. If the maximum value of `I (t)` be `lamda and | lamda| =p/q` where p and q are relatively prime positive integers. Find the product (pq).

Text Solution

Verified by Experts

The correct Answer is:
12
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    VK JAISWAL ENGLISH|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|5 Videos

  • AREA UNDER CURVES

    VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|8 Videos

Similar Questions

Explore conceptually related problems

The value of int_(alpha)^(beta) x|x|dx , where a lt 0 lt beta , is

Let f (x) =(1)/(x ^(2)) int _(4)^(x) (4t ^(2) -2 f '(t) dt, find 9f'(4)

Find the equation whose roots are (alpha)/(beta) and (beta)/(alpha) , where alpha and beta are the roots of the equation x^(2)+2x+3=0 .

Let f(x)=x^(2) +ax + b and the only solution of the equation f(x)= min(f(x)) is x =0 and f(x) =0 "has root " alpha and beta, "then" int _(alpha )^(beta)x^(3) dx is equal to

Consider alpha, beta ,gamma are the roots of x^(3)-x^(2)-3x+4=0 such that tan^(-1)alpha+tan^(-1)beta+tan^(-1)gamma=theta . If the positive value of tan (theta) is p/q, where p and q are natural numbers, then find the value of (p + q) .

Let f(x) be a differentiable function and f(alpha)=f(beta)=0(alpha< beta), then the interval (alpha,beta)

Let f(x) be a function defined by f(x)=int_(1)^(x)t(t^(2)-3t+2)dt,1ltxlt3 then the maximum value of f(x) is

Let alpha, beta be two real roots of the equation cot ^ 2 x - 2 lamda cot x + 3 = 0 , lamda in R . If cot ( alpha + beta ) = (1)/(2) , then value of lamda is :

Let alpha, beta be two real roots of the equation cot ^ 2 x - 2 lamda cot x + 3 = 0 , lamda in R . If cot ( alpha + beta ) = (1)/(2) , then value of lamda is :

Let f (n) = sum _(r =2)^(n) (r )/(""^r C_(2) ""^(r+1) C_(2)) , a = lim _(x to oo) f (n) and x ^(2) -(2n -(1)/(2)) x +t =0 has two positive roots alpha and beta. If value of f (7) + f(8) is p /q where p and q are relatively prime, then (p-q) is :

VK JAISWAL ENGLISH-APPLICATION OF DERIVATIVES -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. If f (x)= (px)/(e ^(x)) - (x ^(2))/(2) + x is a decreasing function f...

    Text Solution

    |

  2. Let f (x)= {{:( xe ^(ax)"," , x le 0),( x+ ax ^(2)-x ^(3)"," , x gt 0)...

    Text Solution

    |

  3. Find sum of all possible values of the real parameter 'b' if the diffe...

    Text Solution

    |

  4. Let 'theta' be the angle in radians between the curves (x ^(2))/(36) +...

    Text Solution

    |

  5. Let set of all possible values of lamda such that f (x)= e ^(2x) - (la...

    Text Solution

    |

  6. Let a,b,c and d be non-negative real number such that a ^(5)+b^(5) le ...

    Text Solution

    |

  7. There is a point (p,q) on the graph of f(x)=x^(2) and a point (r,s) on...

    Text Solution

    |

  8. If f(x)=max| 2 siny-x|, (where y in R), then find the minimum value o...

    Text Solution

    |

  9. Let f (x) = int (0)^(x) ((a -1) (t ^(2)+t+1)^(2) -(a+1)(t^(4)+t ^(2) +...

    Text Solution

    |

  10. The numbr of real roots of the equation x ^(2013)+ e ^(20144x) =0 is

    Text Solution

    |

  11. Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(...

    Text Solution

    |

  12. The least positive vlaue of the parameter 'a' for which there exist at...

    Text Solution

    |

  13. Let f (x) =x ^(2) +2x -t ^(2) and f(x)=0 has two root alpha (t ) and b...

    Text Solution

    |

  14. A tank contains 100 litres of fresh water. S solution containg 1 gm/li...

    Text Solution

    |

  15. If f (x) is continous and differentiable in [-3,9] and f'(x) in [-2,8]...

    Text Solution

    |

  16. It is given that f (x) is defined on R satisfying f (1)=1 and for AA ...

    Text Solution

    |

  17. The number of normals to the curve 3y ^(3) =4x which passes through th...

    Text Solution

    |

  18. Find the number of real root (s) of the equation ae ^(x) =1+ x + (x ^(...

    Text Solution

    |

  19. Let f (x) = ax+cos 2x +sin x+ cos x is defined for AA x in R and a in...

    Text Solution

    |

  20. If p (1) and p(2) are the lengths of the perpendiculars from origin on...

    Text Solution

    |