Home
Class 12
MATHS
For x in R and a continuous function f,...

For `x in R` and a continuous function `f,` let `I_1=int_(sin^2t)^(1+cos^2t)xf{x(2-x)}dx` and `I_2=int_(sin^2t)^(1+cos^2t)f{x(2-x)}dx`.Then `(I_1)/(I_2)` is (a) -1 (b) 1 (c) 2 (d) 3

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise TRUE OR FALSE|1 Videos

Similar Questions

Explore conceptually related problems

Let f be a positive function. Let I_1=int_(1-k)^k xf([x(1-x)])dx , I_2=int_(1-k)^kf[x(1-x)]dx ,w h e r e2k-1> 0. T h e n(I_1)/(I_2)i s 2 (b) k (c) 1/2 (d) 1

If I_1=int_0^pixf(sin^3x+cos^2x)dxand I_2=int_0^(pi/2)f(sin^3x+cos^2x)dx , then relate I_1 and I_2

If I_(1)=int sin^(-1)x dx and I_(2)=int sin^(-1) sqrt(1-x^(2)) dx then -

"I f"I_1=int_(-100)^(101)(dx)/((5+2x-2x^2)(1+e^(2-4x))) "and"I_2=int_(-100)^(101)(dx)/(5+2x-2x^2),t h e n(I_1)/(I_2)"i s" (a)2 (b) 1/2 (c) 1 (d) -1/2

If I_1=int_0^pixf(sin^3x+cos^2x)dxa n d I_2=int_0^(pi/2)f(sin^3x+cos^2x)dx , t h e n r e l a t e I_1 a n d I_2

Let f(x) be a continuous periodic function with period T. Let I= int_(a)^(a+T) f(x)dx . Then

The range of the function f(x)=int_(-1)^(1)(sinxdt)/(1-2tcosx+t^(2)) is

Q. int_0^pie^(cos^2x)( cos^3(2n+1) x dx, n in I

Let I_(1)=int_(0)^(oo)(x^(2)sqrtx)/((1+x)^(6))dx,I_(2)=int_(0)^(oo)(xsqrtx)/((1+x)^(6))dx , then

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. I1=int0^(pi/2)ln(sinx)dx ,I2=int(-pi/4)^(pi/4)ln(sinx+cosx)dxdot Then ...

    Text Solution

    |

  2. Prove that int0^oo[n e^(-x)]dx=ln((n^n)/(n !)),w h e r en is a na...

    Text Solution

    |

  3. For x in R and a continuous function f, let I1=int(sin^2t)^(1+cos^2t)...

    Text Solution

    |

  4. Evaluate of each of the following integrals int(pi//6)^(pi//3)(sqrt...

    Text Solution

    |

  5. Given a function f:[0,4]toR is differentiable ,then prove that for som...

    Text Solution

    |

  6. Evaluate: int0^(pi/2)log((4+3sinx)/(4+3cosx))dx

    Text Solution

    |

  7. The value of int0^1 4x^3 {d^2/(dx^2) (1 - x^2)^5 } dx is

    Text Solution

    |

  8. Evaluate: int(-pi)^(3pi)log(s e c theta-t a ntheta)d theta

    Text Solution

    |

  9. The value of the integral overset(1)underset(0)int e^(x^(2))dx lies in...

    Text Solution

    |

  10. Let P(x) be a polynomial of least degree whose graph has three points ...

    Text Solution

    |

  11. If In=int0^1(dx)/((1+x^2)^n); n in N , then prove that 2nI(n+1)=2^(-n...

    Text Solution

    |

  12. If f(0)=1,f(2)=3,f^'(2)=5,then find the value of int0^1xf^('')(2x)d...

    Text Solution

    |

  13. Ifinta^b(f(x))/(f(x)+f(a+b-x))dx=10 ,t h e n (a) b=22 ,a=2 (b) b=15 ...

    Text Solution

    |

  14. Evaluate: int0^pi(dx)/(1+sinx)

    Text Solution

    |

  15. if In=int0^(pi/4)tan^ntheta.d theta,then n in N,n(I(n-1)+I(n+1)) equal...

    Text Solution

    |

  16. Consider the integral int0^(2pi)(dx)/(5-2cosx) making the substitutio...

    Text Solution

    |

  17. If f(x)=int0^x |t-1| dt, where 0 lt= x lt= 2 then (a) range of f(x) ...

    Text Solution

    |

  18. If int0^1(e^(-x)dx)/(1+e^x)=(log)e(1+e)+k , then find the value of k.

    Text Solution

    |

  19. The value of int0^oo (dx)/(1+x^4) is

    Text Solution

    |

  20. Let f be a continuous function on [a ,b]dot Prove that there exists a ...

    Text Solution

    |