Home
Class 12
MATHS
int (-pi//2)^(pi//2) (dx)/(1+cosx) is e...

` int _(-pi//2)^(pi//2) (dx)/(1+cosx)` is equal to

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
Let `l=int_(-pi//2)^(pi//2)(dx)/(1+cosx)=int_(-pi//2)^(pi//2)(dx)/(2cos^(2).(x)/(2))`
`=int_(0)^(pi//2)sec^(2).(x)/(2)dx=[2tan.(x)/(2)]_(0)^(pi//2)=2`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|22 Videos

  • DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|22 Videos

  • CONTINUITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|16 Videos

  • DIFFERENTIAL EQUATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|27 Videos

Similar Questions

Explore conceptually related problems

int_(-pi/2)^(pi/2)cosx dx

int_(pi//4)^(3pi//4)(dx)/(1+cosx) is equal to

int_(pi//4)^(3pi//4)(dx)/(1+cosx) is equal to

int_(pi//2)^(pi//2)(cosx)/(1+e^(x))dx is equal to

The Integral I=int_(pi/6)^((5pi)/6)(dx)/(1+cosx) is equal to:

int_(pi//4)^(3pi//4)(1)/(1+cosx)dx is equal to

The value of int_(0)^(pi//2)(cosxdx)/(1+cosx+sinx) is equal to

int _(0)^(pi//2) (cosx)/(1+sinx)dx is equal to

Given int_(0)^(pi//2)(dx)/(1+sinx+cosx)=A . Then the value of the definite integral int_(0)^(pi//2)(sinx)/(1+sinx+cosx)dx is equal to

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
  1. int (0)^(pi//4) ( 4 sin 2 theta d theta )/(sin^(4) theta +cos^(4) thet...

    Text Solution

    |

  2. The value of the integral int (-a)^(a) (xe^(x^(2)))/(1+x^(2)) dx is

    Text Solution

    |

  3. int (-pi//2)^(pi//2) (dx)/(1+cosx) is equal to

    Text Solution

    |

  4. The value of int (0)^(12a) (f(x))/(f(x)+f(12a-x))dx is

    Text Solution

    |

  5. If kint(0)^(1)xf(3x)dx=int(0)^(3)tf(t)dt, then the value of k is

    Text Solution

    |

  6. lim(nto oo)+(1)/(sqrt(n^(2)+n))+(1)/(sqrt(n^(2)+2n))+...(1)/(sqrt(n^(2...

    Text Solution

    |

  7. lim(n->oo) (1^p+2^p+3^p+...........+n^p)/n^(p+1)

    Text Solution

    |

  8. Evaluate: ("lim")(nvecoo)(1/(sqrt(4n^2-1))+1/(sqrt(4n^2-2^2))++1/(sqrt...

    Text Solution

    |

  9. If f(x) = tanx-tan ^(3) x + tan^(5) x - tan ^(7) x + ... infty for o...

    Text Solution

    |

  10. The value of int(0)^((pi)/(8))cos^(3)4 theta d theta is equal to -

    Text Solution

    |

  11. int (0)^(pi//3) (cos x + sin x)/(sqrt(1+sin 2x))dx is equal to

    Text Solution

    |

  12. int (0)^(1) x^(3//2) sqrt(1-x) dx is equal to

    Text Solution

    |

  13. The value of int (1)^(2) (dx)/((x+1) sqrt((x^2)-1)) is

    Text Solution

    |

  14. If f(x)=|(sin x+sin x 2x+sin3x,sin2x,sin3x),(3+4sinx,3,4sinx),(1+sinx,...

    Text Solution

    |

  15. int (-1)^(1) (e^(x^(3)) +e^(-x^(3))) (e^(x)-e^(-x)) dx is equal to

    Text Solution

    |

  16. underset(n to oo)lim((1)/(n)+(1)/(n+1)+...+(1)/(3n)) is equal to

    Text Solution

    |

  17. Let f (x) = x – [x], for every real number x, where [x] is the greates...

    Text Solution

    |

  18. The value of int (0)^(1) (x^(4) +1)/(x^(2)+1)dx is

    Text Solution

    |

  19. The value of overset(5)underset(3)int (x^(2))/(x^(2)-4)dx, is

    Text Solution

    |

  20. The value of int (0)^(pi//2) ((sin x + cos x)^(2))/(sqrt(1+sin 2x) dx...

    Text Solution

    |