Home
Class 12
MATHS
underset(0)overset(1)intlnsin(pi/2x) dx...

`underset(0)overset(1)intlnsin(pi/2x) dx`

A

`ln2`

B

`-ln 2`

C

`pi ln 2`

D

`-pi ln2`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Main (Archive)|64 Videos
  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|103 Videos
  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|103 Videos
  • FUNCTIONS

    VMC MODULES ENGLISH|Exercise JEE Main & Advanced|8 Videos
  • INTEGRAL CALCULUS-1

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|25 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following definite integrals underset(0)overset(pi//2)intsin^(2)xdx

Evaluate: underset(0)overset(pi//4)intsinxdx

Evaluate the following definite integrals underset(0)overset(1//2)intsqrt(19+4x)dx

If f(x)={{:(x,xlt1),(x-1,xge1):} , then underset(0)overset(2)intx^(2)f(x) dx is equal to :

The following functions are continuous on (0, pi) (a) tan x (b) underset(0)overset(x)int t "sin"(1)/(t)dt (c) {{:(,-1,0 lt xle (3pi)/(4)),(,2sin((2)/(9)x),(3pi)/(4)lt xlt pi):} (d) {{:(,x sin x,0 lt x le (pi)/(2)),(,(pi)/(2)sin(pi+x),(pi)/(2)lt x lt pi):}

The value of underset(0)overset(pi//2)int (sin^(3)x)/(sin x + cos x)dx is (pi-1)/(k) . The value of k is ________.

The value of (.^(n)C_(0))/(n)+(.^(n)C_(1))/(n+1)+(.^(n)C_(2))/(n+2)+"..."+(.^(n)C_(n))/(2n) (a) underset(0)overset(1)intx^(n-1)(1+x)^(n)dx (b) underset(1)overset(2)intx^(n)(x-1)^(n-1)dx (c) underset(1)overset(2)int(1+x)^(n)dx (d) underset(0)overset(1)int(1-x)^(n)x^(n-1)dx

int_(0)^(1) lnsin(pi/2x) dx

Area bounded by the curves y = 1 - 2^(1 + sin x), x in [0, (pi)/(2)] where underset(0)overset(pi//2)(int) 2^(sin x) dx = k

The value of the integral underset(0)overset(1)int cot^(-1) (1-x+x^(2))dx , is

VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -Level - 1
  1. if I = int0 ^1.7 [x^2]dx, then I equal is

    Text Solution

    |

  2. I1=int0^(pi/2)ln(sinx)dx ,I2=int(-pi/4)^(pi/4)ln(sinx+cosx)dxdot Then ...

    Text Solution

    |

  3. underset(0)overset(1)intlnsin(pi/2x) dx

    Text Solution

    |

  4. If int(1/2)^2 1/x cosec^(101)(x-1/x)dx=k then the value of k is :

    Text Solution

    |

  5. The value of overset(16pi//3)underset(0)int |sinx|dx is

    Text Solution

    |

  6. The value of int(0)^(1000)e^(x-[x])dx, is ([.] denotes the greatest in...

    Text Solution

    |

  7. Evaluate (int(0)^(n)[x]dx)/(int(0)^(n){x}dx) (where [x] and {x} are in...

    Text Solution

    |

  8. Evaluate: inta^b e^x dx using limit of sum

    Text Solution

    |

  9. Evaluate: inta^bsinx dx using limit of sum

    Text Solution

    |

  10. lim(n to oo)(1)/(n)(1+sqrt((n)/(n+1))+sqrt((n)/(n+2))+....+sqrt((n)/(4...

    Text Solution

    |

  11. Evaluate lim(n->oo)1/nsum(r=n+1)^(2n)loge(1+r/n)

    Text Solution

    |

  12. The value of lim(n to oo)((1)/(1^(3)+n^(3))+(2^(2))/(2^(3)+n^(3))+.......

    Text Solution

    |

  13. Evaluate : lim(n to oo)[(sqrt(n))/((3+4sqrt(n))^(2))+(sqrt(n))/(sqrt(2...

    Text Solution

    |

  14. lim(n->oo)[1/sqrt(2n-1^2) +1/sqrt(4n-2^2)+1/sqrt(6n-3^2)+...+1/n]

    Text Solution

    |

  15. The value of lim(n to oo)[(n)/(n^(2))+(n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(...

    Text Solution

    |

  16. lim(n to oo)((1)/(1+n^(3))+(4)/(8+n^(3))+....+(r^(2))/(r^(3)+n^(3))+.....

    Text Solution

    |

  17. lim(n to oo)[(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+....+(1)/(n)]

    Text Solution

    |

  18. underset(nrarroo)("lim")[(1+(1)/(n^(2)))(1+(2^(2))/(n^(2)))"....."(1+(...

    Text Solution

    |

  19. lim(n to oo)[(sqrt(n+1)+sqrt(n+2)+....+sqrt(2n))/(n sqrt((n)))]

    Text Solution

    |

  20. IfSn=[1/(1+sqrt(n))+1/(2+sqrt(2n))++1/(n+sqrt(n^2))],t h e n(lim)(n ra...

    Text Solution

    |