Home
Class 12
MATHS
If I1=int0^pixf(sin^3x+cos^2x)dxa n d I...

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 nr e l a t eI_1a n dI_2`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE ENGLISH|Exercise MATRIX-MATCH TYPE|3 Videos

Similar Questions

Explore conceptually related problems

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

int_0^(pi/2) sin^3x/(sin^3x+cos^3x)dx

I=int_0^(2pi) e^(sin^2x+sinx+1)dx then

Evaluate: int_0^(pi//2)1/(4sin^2x+5cos^2x)dx

If I_n = int_0^(pi/2) (sin^2 nx)/(sin^2 x) dx , then

Evaluate: int_0^(pi//2)(sin x)/(1+cos^2x)dx

IfI_1=int_0^(pi/2)(cos^2x)/(1+cos^2x)dx ,I_2=int_0^(pi/2)(sin^2x)/(1+sin^2x)dx I_3=int_0^(pi/2)(1+2cos^2xsin^2x)/(4+2cos^2xsin^2x)dx ,t h e n I_1=I_2> I_3 (b) I_3> I_1=I_2 I_1=I_2=I_3 (d) none of these

If I_(1)=int_(3pi)^(0) f(cos^(2)x)dx and I_(2)=int_(pi)^(0) f(cos^(2)x) then

If I_1=int_0^(pi//2)(cos^2x)/(1+cos^2x)dx , I_2=int_0^(pi//2)(sin^2x)/(1+sin^2x)dx and I_3=int_0^(pi//2)(1+2cos^2xsin^2x)/(4+2cos^2xsin^2x)dx , then (a) I_1=I_2 > I_3 (b) I_3> I_1=I_2 (c) I_1=I_2=I_3 (d) none of these

IfI_I=int_0^(pi//2)cos(sinx)dx ,I_2=int_0^(pi/2)sin(cosx)d ,a n dI_3=int_0^(pi/2)cosx dx , then find the order in which the values I_1,I_2,I_3, exist.

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. Match the statements/expression given in Column I with the values give...

    Text Solution

    |

  2. If int0^t(bxcos4x-asin4x)/(x^2)=(asin4t)/t-1 where 0lttltpi/4, then th...

    Text Solution

    |

  3. If I1=int0^pixf(sin^3x+cos^2x)dxa n d I2=int0^(pi/2)f(sin^3x+cos^2x)d...

    Text Solution

    |

  4. int0^(pi/2)(sqrt(sinx))/(sqrt(sinx)+sqrt(cosx)) dx

    Text Solution

    |

  5. If Un=int0^1x^n(2-x)^ndxa n dVn=int0^1x^n(1-x)^n dx ,n in N , and if ...

    Text Solution

    |

  6. Find the value of int0^1 2x^3-3x^2-x+1 3dxdot

    Text Solution

    |

  7. If int0^oox^(2n+1)dote^(-x^2)dx=360 , then the value of n is

    Text Solution

    |

  8. Evaluate: int0^oo(dx)/(1+x^2)

    Text Solution

    |

  9. Iflambda=int0^(pi/2)costhetaf(sintheta+cos^2theta)dtheta a n dI2=int0...

    Text Solution

    |

  10. If f(a+b-x)=f(x), then prove that inta^b xf(x)dx=(a+b)/2inta^bf...

    Text Solution

    |

  11. Let I1=int(-2)^2(x^6+3x^5+7x^4)/(x^4+2)dx and I2=int(-3)^1(2(x+1)^2+1...

    Text Solution

    |

  12. Find the value of int0^(pi/2)sin2xdx

    Text Solution

    |

  13. The value of int0^(pi/2)cos^2xdx

    Text Solution

    |

  14. prove that |sint| is non-differentiable at t=pi.

    Text Solution

    |

  15. Find the value of int0^1x(1-x)dx

    Text Solution

    |

  16. Let Sn=sum(k=0)^n n/(n^2+kn+k^2) and Tn=sum(k=0)^(n-1) n/(n^2+kn+k^2) ...

    Text Solution

    |

  17. The value of the definite integral int(sqrt2-1)^(sqrt(2)+1)(x^4+x^2+2...

    Text Solution

    |

  18. If a continuous function f on [0, a] satisfies f(x)f(a-x)=1, a >0, the...

    Text Solution

    |

  19. L e tJ=int(-5)^(-4)(3-x^2)tan(3-x^2)dx and K=int(-2)^(-1)(6-6x+x^2) t...

    Text Solution

    |

  20. Let g(x) be differentiable on R and int(sint)^1x^2g(x)dx=(1-sint), wh...

    Text Solution

    |