Home
Class 12
MATHS
Let f(x)=[b^(2)+(a-1)b+2]x-int(sin^(2)x+...

Let `f(x)=[b^(2)+(a-1)b+2]x-int(sin^(2)x+cos^(4)x)dx` be an increasing function of `x""inRandbinR`, then a can take value(s)

Promotional Banner

Topper's Solved these Questions

  • Properties and Application of definite Integrals

    A DAS GUPTA|Exercise EXERCISE|62 Videos

  • Progression, Related Inequalities and Series

    A DAS GUPTA|Exercise Exercise|235 Videos

  • Recap of Facts and Formulae

    A DAS GUPTA|Exercise Exercise|9 Videos

Similar Questions

Explore conceptually related problems

If f(x)={b^(2)+(a-1)b+2}x-int(sin^(2)x+cos^(4)x)dx be an increasing function of xepsilonR and bepsilonR , then a can take value (s)

f(x)=[-c^(2)+(b-1)c-2)]x+int(sin^(2)x+cos^(4)x)dx If f(x) be an increasing function of x AA x in R then all possible values of b if (c in R)

Let f(x)={b^(2)+(a-1)b-(1)/(4)}x+int_(0)^(x)(sin^(4)theta+cos^(4)theta)d theta If f(x) be a non- decreasing function AA x in R and AA b in R then "a" can belong to

int(a sin^(3)x+b cos^(3)x)/(sin^(2)x cos^(2)x)dx

int(a sin^(3)x-b cos^(3)x)/(sin^(2)x cos^(2)x)dx

int(1)/(4sin^(2)x+4sin x cos x+5cos^(2)x)dx

Let int(xsinx)/((x cos x-sin x)^(2))dx then

Let f(x) = inte^(x^(2))(x-2)(x-3)(x-4)dx then f increases on

Let F(x)=(1)/(2)int(sin x+cos x)/(e^(-x)+sin x)dx and F(0)=1 then F(x) is

Let f(x)=int e^(x^(2))(x-2)(x-3)(x-4)dx then f increases on (k,k+1) then k is

A DAS GUPTA-Properties and Application of definite Integrals-EXERCISE
  1. State whether the statements are true or false.If y=int0^xf(t)dt .Then...

    Text Solution

    |

  2. State whether the statements are true or false.int0^(pi/2)dx/(sqrt(sin...

    Text Solution

    |

  3. If int0^a{f(x)+f(-x)}dx=int-a^aphi(x)dxthen phi(x)=.

    Text Solution

    |

  4. Evaluate: int0^pi (cos x)/(1+sinx)^2 dx

    Text Solution

    |

  5. The value int(-pi/4)^(pi/4)x^2sin^-1xdx=.

    Text Solution

    |

  6. If int0^pi x f(sinx) dx=A int0^(pi/2) f(sinx)dx, then A is (A) pi/2 (B...

    Text Solution

    |

  7. The value of int0^(pi/2)sin2x.log tanxdx is

    Text Solution

    |

  8. If int0^1e^t/(t+1) dt=a, then int(b-1)^b e^(-t)/(t-b-1) dt=

    Text Solution

    |

  9. Evaluateint(-pi/2)^(pi/2)(sin2x)/(1+cos^3x)dx

    Text Solution

    |

  10. If f is a continuous function on the interval [a,b] and there exists ...

    Text Solution

    |

  11. If l(n)=int(1)^(e)(log x)^(n) d x, "then" l(n)+nl(n-1) equal to

    Text Solution

    |

  12. If f(x)=|x-21|+|x-1|then evaluate int-2^2f(x)dx.

    Text Solution

    |

  13. If f(x)=f(4-x), g(x)+g(4-x)=3 and int(0)^(4)f(x)dx=2, then : int(0)^(4...

    Text Solution

    |

  14. It is known that f(x) is an odd function and has a period p. Prove tha...

    Text Solution

    |

  15. The value of int(0)^(2)x^([x^(2)+1])(dx), where [x] is the greatest in...

    Text Solution

    |

  16. Let f(x)=[b^(2)+(a-1)b+2]x-int(sin^(2)x+cos^(4)x)dx be an increasing f...

    Text Solution

    |

  17. For x >0,l e tf(x)=int1^x(logt)/(1+t)dtdot Find the function f(x)+f(1/...

    Text Solution

    |

  18. If overset(1)underset(0)int(sint)/(1+t)dt=alpha, them the value of the...

    Text Solution

    |

  19. Evaluate: int0^(pi/2) sin^2x/(sinx+cosx)dx

    Text Solution

    |

  20. The point of extremum of f(x)=int0^x(t-2)^2(t-1)dt is a

    Text Solution

    |