Home
Class 12
MATHS
For theta in (0,pi/2), prove that int0^t...

For `theta in (0,pi/2)`, prove that `int_0^theta"log"(1+tanthetatanx)dx=thetalog(sectheta)`

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

Evaluate: int_(0)^((pi)/(4))log(1+tantheta)d theta

Evalute: int_(0)^((pi)/(4)) log(1+tantheta)d theta .

int_(0)^(pi)(sin4theta)/(sintheta)d theta=0

Prove that: (cos2theta)/(1+sin2theta)=tan(pi/4-theta)

Prove that (cos2theta)/(1+sin2theta)=tan(pi/4-theta) .

Find lim_(theta to 0)theta log(2-cos^2 theta)

Show that sectheta+tantheta=tan(pi/4+theta/2)

prove that, sqrt((sectheta-1)/(sectheta+1))="cosec"theta-cottheta.

int_(0)^((pi)/(4))thetasec^(2)thetad theta

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

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. int 0^(pi/2) (sin^2x)/(sinx+cosx)dx

    Text Solution

    |

  2. The value of the definite integral int0^(pi/2)sqrt(tanx)dx is (a) s...

    Text Solution

    |

  3. For theta in (0,pi/2), prove that int0^theta"log"(1+tanthetatanx)dx=th...

    Text Solution

    |

  4. A function f is defined by f(x)=1/(2^(r-1)),1/(2^r)ltxlt=1 (2^(r-1)),...

    Text Solution

    |

  5. Evaluate int0^1(dx)/((5+2x-2x^2)(1+e^(2-4x))) dx

    Text Solution

    |

  6. If P(x) is a polynomial of the least degree that has a maximum equal t...

    Text Solution

    |

  7. Evaluate: int0^pixlogsinxdx

    Text Solution

    |

  8. The value of the definite integral int0^(sqrt(1n(pi/2)))cose^(x^(2)...

    Text Solution

    |

  9. Evaluate: int0^(π/2)cos2x+4sin2x cos2xdx

    Text Solution

    |

  10. The value of int1^((1+sqrt(5))/2)(x^2+1)/(x^4-x^2+1)log(1+x-1/x)dx is...

    Text Solution

    |

  11. If f(x) is a function satisfying f(x+a)+f(x)=0 for all x in R and pos...

    Text Solution

    |

  12. If f(x) is monotonic differentiable function on [a , b] , then int...

    Text Solution

    |

  13. L e tA=int0^oo(logx)/(1+x^3)dx Then find the value of int0^oo(xlogx)/(...

    Text Solution

    |

  14. Show that : int0^1(logx)/((1+x))dx=-int0^1(log(1+x))/x dx

    Text Solution

    |

  15. The value of lim(n->oo) [tan(pi/(2n)) tan((2pi)/(2n))........tan((npi...

    Text Solution

    |

  16. answer any one question : (ii) evaluate : int0^pi (x sin x)/(1+cos ^2x...

    Text Solution

    |

  17. Match the statements/expression given in Column I with the values give...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |