Home
Class 12
MATHS
Let f(x)=x^(2) +ax + b and the only sol...

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

A

`(1)/(4) ( beta ^(4) + alpha ^(4))`

B

`(1)/(4)( a^(2)- b^(2))`

C

0

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
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

If y=f(x) and y=g(x) are symmetrical about the line x=(alpha+beta)/(2), then int_(alpha)^( beta)f(x)g'(x)dx is equal to

Let alpha , beta be the roots of the equation (x-a) (x-b) = c , cne 0 , then find the roots of the equation (x - alpha) (x -beta) + c = 0

If root of the equation x^(2) + ax + b = 0 are alpha , beta , then the roots of x^(2) + (2 alpha + a) x + alpha^(2) + a alpha + b = 0 are

Let f (x) be a conitnuous function defined on [0,a] such that f(a-x)=f(x)"for all" x in [ 0,a] . If int_(0)^(a//2) f(x) dx=alpha, then int _(0)^(a) f(x) dx is equal to

Let f(x) = ax^(2) + bx + c, a, b, c, in R and equation f(x) - x = 0 has imaginary roots alpha, beta . If r, s be the roots of f(f(x)) - x = 0 , then |(2,alpha,delta),(beta,0,alpha),(gamma,beta,1)| is

Let f(x)=int_1^x(3^t)/(1+t^2)dx ,w h e r e x > 0. Then (a)for 0

If f(x)=27x^(3)+(1)/(x^(3)) and alpha,beta are the roots of the equation 3x+(1)/(x)=2, then -f(alpha) is equal to

Let f(x) be a differentiable function and f(alpha)=f(beta)=0(alpha

If alpha and beta are the roots of the equation x^(2)-3x-15=0 and (n)=alpha^(n)+beta^(n) then find the value of (f(8)-3f(7)+f(6))/(2f(6))

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Single Option Correct Type Questions)
  1. int(0)^(4)((y^(2)-4y+5)sin(y-2)dy)/([2y^(2)-8y+1]) is equal to

    Text Solution

    |

  2. Let f(x)=x^(2) +ax + b and the only solution of the equation f(x)= mi...

    Text Solution

    |

  3. Ifint(pi/3)^xsqrt((3-sin^2t))dt+int0^ycostdt=0,t h e ne v a l u a t e(...

    Text Solution

    |

  4. int(-4)^(4) (sin^(-1)( sinx)+ cos^(-1)(cos x))/((1+x^(2))(1+[(x^(2))/(...

    Text Solution

    |

  5. The value of the definite integral int (0)^(infty) (dx)/((1+x^(a))(1...

    Text Solution

    |

  6. The value of the definite integral overset(3pi//4)underset(0)int(1+x)s...

    Text Solution

    |

  7. Let C(n)= int(1//n+1)^(1//n)(tan^(-1)(nx))/(sin^(-1) (nx)) dx , "then ...

    Text Solution

    |

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

    Text Solution

    |

  9. If f(x) = e^(g(x)) and g (x) = int2 ^x dt/(1+t^4) then f' (2) is equa...

    Text Solution

    |

  10. If a, b and c are real numbers, then the value of lim(t to 0) In ((1)/...

    Text Solution

    |

  11. The value of lim(n to oo) sum(r=1)^(r=4n) (sqrtn)/(sqrt(r(3sqrtr+4sqrt...

    Text Solution

    |

  12. Let f(x) =int-1^x e^(t^2) dt and h(x)=f(1+g(x)), where g (x) is define...

    Text Solution

    |

  13. Let f(x) be a function satisfying f\'(x)=f(x) with f(0)=1 and g(x) be ...

    Text Solution

    |

  14. Let f(x)=int0^g(x) dx/sqrt(1+t^2) where g(x) =int0^cosx (1+sint^2) dt....

    Text Solution

    |

  15. For f(x) =x^(4) +|x|, let I(1)= int (0)^(pi)f(cos x) dx and I(2)= int(...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |