Home
Class 12
MATHS
int0 ^ (pi/2) log(cosx) dx=...

`int_0 ^ (pi/2) log(cosx) dx=`

A

`pi/2 log(1/2)`

B

`1-pi/2 log(1/2)`

C

`1+pi/2 log (1/2)`

D

`pi/2 log 2`

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `int_(0)^(pi/2) log cos x dx = (pi)/(2) log '1/2 "…"(i)`
Let `I = int_(0)^(pi/2) log sec x dx = int_0^(pi/2) log(1/(cosx)) dx`
`= int_(0)^(pi/2) log(cosx)^(-1) dx = -int_(0)^(pi/2) log (cos x) dx`
`= I int_(0)^(pi/2) log (cos x) dx [ :' log m^(-n) = - nlogm]`
`= - pi/2 log(1/2) ( :' log(1/a) = - log a)`
` = pi/2 log 2`
Promotional Banner

Topper's Solved these Questions

  • MHTCET 2016

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Mathematics|50 Videos

  • MHTCET 2018

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Mathematics|50 Videos

Similar Questions

Explore conceptually related problems

int_(0)^(pi//2) log (cotx ) dx=

Prove that: int_(0)^(pi//2) log (sin x) dx =int_(0)^(pi//2) log (cos x) dx =(-pi)/(2) log 2

If int_(0)^(pi//2) log cos x dx =(pi)/(2)log ((1)/(2)), then int_(0)^(pi//2) log sec x dx =

Evaluate int_0^(pi/2)sinx.log cosx dx

Consider is int_(0)^(pi//2) ln (sinx)dx equal to ? What is int_(0)^(pi//2) ln (cos x) dx equal to ?

Prove that: int_0^(pi//2)logsinx\ dx=\ int_0^(pi//2)logcosx\ dx=-pi/2log2

int_(0)^(pi)log(1+cosx)dx=-pi(log2)

int_0^(pi//2)log(tanx)dx

int_0^(pi/2) (Cosx - Sinx)dx

Evaluate the following: int_0^(pi/2) cosx/(cosx+sinx)dx

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-MHTCET 2017-MATHMATICS
  1. If x=f(t) and y=g(t) , then write the value of (d^2y)/(dx^2) .

    Text Solution

    |

  2. The equation of line equally inclined to coordinate axes and passing t...

    Text Solution

    |

  3. int0 ^ (pi/2) log(cosx) dx=

    Text Solution

    |

  4. A boy tosses faiir coin 3 times. If he gets Rs 2X for X heads, then hi...

    Text Solution

    |

  5. Which of the following statement pattern is a tautology?

    Text Solution

    |

  6. If the angle between the planes r.(mhati-hatj+2hatk)+3=0 and r*(2hati-...

    Text Solution

    |

  7. If the origin and the points P(2,3,4), Q(1,2,3) and R(x,y,z) are copla...

    Text Solution

    |

  8. if lines represented by equation px^(2)-qy^(2)=0 are distinct, then

    Text Solution

    |

  9. Let square PQRS be a quadrilateral. If M and N are the mid-points of t...

    Text Solution

    |

  10. If slopes of lines represented by kx^(2)+5xy+y^(2)=0 differ by 1, then...

    Text Solution

    |

  11. If vector r wiith dc's l,m,n is equally inclined to the coordinate axe...

    Text Solution

    |

  12. If int(1)/((x^(2)+4)(x^(2)+9))dx=A" tan"^(-1)(x)/(2)+Btan^(-1)((x)/(3)...

    Text Solution

    |

  13. If alpha and beta are roots of the equation x^(2)+5|x|-6=0, then the v...

    Text Solution

    |

  14. If x=a(t-(1)/(t)),y=a(t+(1)/(t)), where t be the parameter, then (dy)/...

    Text Solution

    |

  15. The point on the curve y=sqrt(x-1), where the tangent is perpendicular...

    Text Solution

    |

  16. If intsqrt((x-5)/(x-7))dx = A sqrt(x^(2) - 12 x + 35) + log|x-6 +sqr...

    Text Solution

    |

  17. At random variable X~B(n,p) if values of mean and variance of X are 18...

    Text Solution

    |

  18. The area of the region bounded by the lines y=2x+1y=3x+1 and x=4 is

    Text Solution

    |

  19. A box contains 6 pens, 2 of which are defective. Two pens are taken r...

    Text Solution

    |

  20. If the volume of spherical ball is increasing at the rate of 4pi" cc/s...

    Text Solution

    |