Home
Class 12
MATHS
If I1=int0^(pi/2)costhetaf(sintheta+cos^...

`If I_1=int_0^(pi/2)costhetaf(sintheta+cos^2theta)d(theta)` `and I_2=int_0^(pi//2)sin2thetaf(sintheta+cos^2theta)d(theta)`, then
(a) `I_1=-2I_2` (b) `I_1=I_2` (c) `2I_1=I_2` (d) `I_1=-I_2`

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

if I=int_0^(pi/4) (sin2theta)/(sin^2theta+cos^4theta)d(theta) then I equals

int_(0)^((pi)/(2))(sin^(3)theta)/(sin^(3)theta+cos^(3)theta)d theta

int(cos2theta)/((sintheta+costheta)^2)d theta is equal to

Show that int_0^(pi/2)sqrt((sin2theta))sintheta d theta=pi/4

If int_0^(pi/2)logsinthetad(theta)=k , then find the value of int_0^(pi/2)(theta/(sintheta))^2d(theta) in terms of k

Let f beintegrable over [0,a] for any real value of a . If I_(1)=int_(0)^(pi//2)cos theta f(sin theta +cos^(2) theta) d theta and I_(2)=int_(0)^(pi//2) sin 2 theta f(sin theta+cos^(2) theta) d theta , then

I_1=int_0^(pi/2)ln(sinx)dx ,I_2=int_(-pi/4)^(pi/4)ln(sinx+cosx)dxdot Then (a) I_1=2I_2 (b) I_2=2I_1 I_1=4I_2 (d) I_2=4I_1

int (sin^(2)theta d theta)/((1 + cos theta)^(2))

I=intcos^3(2theta)d theta is equal to

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

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. If int0^oox^(2n+1)dote^(-x^2)dx=360 , then the value of n is

    Text Solution

    |

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

    Text Solution

    |

  3. If I1=int0^(pi/2)costhetaf(sintheta+cos^2theta)d(theta) and I2=int0^(...

    Text Solution

    |

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

    Text Solution

    |

  5. 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

    |

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

    Text Solution

    |

  7. Let f:[a,b]rarr[1,infty) be a continuous function and lt g: RrarrR be ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. 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

    |

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

    Text Solution

    |

  16. Show that ("lim")(n vec oo)(1/(n+1)+1/(n+2)++1/(6n))=log6

    Text Solution

    |

  17. int(-pi/3)^0[cot^(-1)(2/(2cosx-1))+cot^(-1)(cosx-1/2)]dx i s equal to...

    Text Solution

    |

  18. Ifint(-pi/4)^((3pi)/4)(e^(pi/4)dx)/((e^x+e^(pi/4))(sinx+cosx))=kint(-p...

    Text Solution

    |

  19. If f(x) =(e^x)/(1+e^x), I1=int(f(-a))^(f(a)) xg(x(1-x))dx, and I2=int(...

    Text Solution

    |

  20. If f(y)=e^y ,g(y) = y>0,a n d \ F(t)=int0^t f(t-y)g(y)dy ,then

    Text Solution

    |