Home
Class 12
MATHS
Let a, b and c be non - zero real number...

Let a, b and c be non - zero real numbers such that ` int _(0)^(3) (3ax ^(2) + 2bx +c) dx = int _(1)^(3) (3ax^(2) + 2bx +c) dx` , then

A

`a+b+c=3`

B

`a+b+c=1`

C

`a+b+c=0`

D

`a+b+c=2`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    TARGET PUBLICATION|Exercise EVALUATIO TEST|30 Videos
  • DEFINITE INTEGRALS

    TARGET PUBLICATION|Exercise CRITICAL THINKING|115 Videos
  • CONTINUITY

    TARGET PUBLICATION|Exercise Evaluation Test|10 Videos
  • DIFFERENTIAL EQUATIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|25 Videos

Similar Questions

Explore conceptually related problems

Let a,b,c be non-zero real numbers such that int_(0)^(1)(1+cos^(8)x)(ax^(2)+bx+c)dx=int_(0)^(2)(1+cos^(8)x)(ax^(2)+bx+c)dx then the quadratic equation ax^(2)+bx+c=0 has -

Let a, b, c be non zero numbers such that int_(0)^(3)sqrt(x^(2)+x+1)(ax^(2)+bx+c)dx=int_(0)^(5)sqrt(1+x^(2)+x)(ax^(2)+bx+c)dx . Then the quadratic equation ax^(2)+bx+c=0 has

Let a,b,c be nonzero real numbers such that int_(0)^(1)(1+cos^(8)x)(ax^(2)+bx+c)dx=int_(0)^(2)(1+cos^(8)x)(ax^(2)+bx+c)dx=0 Then show that the equation ax^(2)+bx+c=0 will have one root between 0and 1 and other root between 1 and 2.

Evaluate int_(1)^(4) (ax^(2)+bx+c)dx .

Let a, b, c be non-zero real roots of the equation x^(3)+ax^(2)+bx+c=0 . Then

Let a,b and c be real numbers such that 4a+2b+c=0 and ab<0. Then the equation ax^(2)+bx+c=0

int(ax^(2)+bx+c)^(2)dx

Let a, b and c be real numbers such that 4a + 2b + c = 0 and ab gt 0. Then the equation ax^(2) + bx + c = 0 has

TARGET PUBLICATION-DEFINITE INTEGRALS-COMPETITIVE THINKING
  1. int(0)^(1)(sin^(-1)(x/2))/xdx=

    Text Solution

    |

  2. If I(1)=overset(e^(2))underset(e )int(dx)/(logx)"and "I(2)=overset(2)u...

    Text Solution

    |

  3. Let a, b and c be non - zero real numbers such that int (0)^(3) (3ax...

    Text Solution

    |

  4. If int(-1) ^(4) f(x) dx=4and int(2)^(4) (3-f(x))dx=7, then int(-1) ^...

    Text Solution

    |

  5. Ifg(x)= int(0)^(x) cos 4t dt, "then " g (x+pi) equals

    Text Solution

    |

  6. if f(x)=|x-1| then int(0)^(2)f(x)dx is

    Text Solution

    |

  7. int- 5^5|x+2|dx

    Text Solution

    |

  8. If f(x)=int(-1)^(x)|t|dt, then for any x ge0,f(x) is equal to

    Text Solution

    |

  9. int(0)^(1)|3x-1|dx=

    Text Solution

    |

  10. int-2^2 |1-x^2|dx= (A) 4 (B) 2 (C) -2 (D) 0

    Text Solution

    |

  11. The value of int(0)^(1)x|x-1/2|dx is

    Text Solution

    |

  12. int(0)^(100pi)|cosx|dx=…………………………..

    Text Solution

    |

  13. int(0)^(pi//2) abs(sinx-cosx) dx=

    Text Solution

    |

  14. The integral int(0)^(pi)sqrt(1+4"sin"^2(x)/(2)-4"sin"(x)/(2)) dx is e...

    Text Solution

    |

  15. If I=int(1/ e)^e|logx|(dx)/(x^2) ,then I equals (A) 2 (B) 2...

    Text Solution

    |

  16. int(0) ^(3) [x] dx= where [x] is greatest integer function

    Text Solution

    |

  17. Let f(x) = x-[x], for every real number x, where [x] is integral part ...

    Text Solution

    |

  18. The integral int0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest ...

    Text Solution

    |

  19. The value of int0^9[sqrt(x)+2]dx, where [.] is the greatest integer fu...

    Text Solution

    |

  20. If for all real numbers y ,[y] is the greatest integer less than or eq...

    Text Solution

    |