Home
Class 12
MATHS
The value of I = int0^(pi//2) ((sin x + ...

The value of `I = int_0^(pi//2) ((sin x + cos x)^2)/(sqrt(1 + sin 2x)) dx` is :

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSTEMS, LOCUS AND STRAIGHT LINES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|297 Videos

  • DIFFERENTIAL EQUATIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|206 Videos

Similar Questions

Explore conceptually related problems

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

int_0^(pi//4) (sin x + cos x)/(3 + sin 2x ) dx =

int_0^(pi/2) sin^(2)x dx =

int_(0)^(pi//2) (sin x)/(1 +cos^2) dx .

int_0^(pi//2)(sqrt(sin x))/(sqrt(sin x) + sqrt(cos x)) dx equals:

int_0^(2pi) sqrt(1 + sin( x/2)) dx is :

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

The value of the integral int_0^(pi//2) (sin^(100) x - cos^(100) x) dx is :

HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
  1. Let f(x) be a function satisfying f'(x) = f(x) with f(0) = 1 and g(x) ...

    Text Solution

    |

  2. If f(x) = (e^x)/(1 + e^x) , I1 = int(f(-a))^(f(a)) x g {x(1 - x)} dx a...

    Text Solution

    |

  3. The value of I = int0^(pi//2) ((sin x + cos x)^2)/(sqrt(1 + sin 2x)) d...

    Text Solution

    |

  4. The value of int(-2)^3 |1 - x^2| dx is:

    Text Solution

    |

  5. If int0^pi x f (sin x)dx = A int0^(pi//2) f (sin x) dx, then A is :

    Text Solution

    |

  6. Let F : R to R be a differentiable function having : f(2) = 6, f'(2) =...

    Text Solution

    |

  7. int0^(pi) x f (sin x) dx is equal to :

    Text Solution

    |

  8. int(-3pi//2)^(-pi//2) [(x +pi)^3 + cos^2 (x + 3x)]dx is equal to :

    Text Solution

    |

  9. If f(x) ={(e^(cosx)sinx; |x| le 2),(2 ; othe...

    Text Solution

    |

  10. The value of integral int(e^(-1))^(e^2) |(loge x)/(x)| dx is :

    Text Solution

    |

  11. Let g(x) = int0^(x) f(t) dt, where 1/2 le f(t) < 1, t in [0,1] and 0 <...

    Text Solution

    |

  12. The value of int(-pi)^(pi) (cos^2 x)/(1 + a^x) dx, a > 0, is :

    Text Solution

    |

  13. Let f : (0, oo ) to R and F(x) = int0^x f(t) dt. If F(x^2) = x^2(1 +...

    Text Solution

    |

  14. Let f(x) = int1^x sqrt(2 - t^2) dt. Then the real roots of the equatio...

    Text Solution

    |

  15. The integral int(-1//2)^(1//2) ([x] + ln ((1 + x)/(1 - x)))dx equals :

    Text Solution

    |

  16. If I(m,n) = int0^1 t^m (1 + t)^n dt , m, n in R, then I(m, n) is :

    Text Solution

    |

  17. The value of the integral int0^1 sqrt((1 - x)/(1 + x))dx is :

    Text Solution

    |

  18. If f(x) is differentiable and int0^(t^2) x f(x) dx = 2/5 t^5, then f (...

    Text Solution

    |

  19. If int(sin x)^(1) t^2 f(t) dt = 1 - sin x, then the value of f(1/(sqrt...

    Text Solution

    |

  20. int(-2)^(0) {x^3 + 3x^2 + 3x + 3 + (x + 1) cos (x + 1)} dx is equal to...

    Text Solution

    |