Home
Class 12
MATHS
The value of int(-2)^(2)(sin^(2)x)/([(x)...

The value of `int_(-2)^(2)(sin^(2)x)/([(x)/(pi)]+(1)/(2))dx` where [.] denotes greatest integer function , is

A

1

B

0

C

`4 - sin 4`

D

None of these

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

int_(-1)^(2)[([x])/(1+x^(2))]dx , where [.] denotes the greatest integer function, is equal to

The value of int_(e)^(pi^(2))[log_(pi)x] d(log_(e)x) (where [.] denotes greatest integer function) is

The value of int_(-2)^1[x[1+cos((pix)/2)]+1]dx , where [.] denotes the greatest integer function, is (a)1 (b) 1//2 (c) 2 (d) none of these

The value of lim_(xrarr(pi)/(2))([(x)/(3)])/(ln(sinx)) (where, [.] denotes the greatest integer function)

The value of int_(-20pi)^(20 pi) |sin x| [ sin x] dx is (where [.] denotes greatest integer function)

int_(0)^([x]//3) (8^(x))/(2^([3x]))dx where [.] denotes the greatest integer function, is equal to

Evaluate int_(4)^(6)([x^(2)])/([x^(2)-20x+100]+[x^(2)])dx where [.] denotes the greatest integer function.

The value of int_(-pi//2)^(pi//2)[ cot^(-1)x] dx (where ,[.] denotes greatest integer function) is equal to

The value of the integral int_(-2)^2 sin^2x/(-2[x/pi]+1/2)dx (where [x] denotes the greatest integer less then or equal to x) is

The value of int _(1)^(2)(x^([x^(2)])+[x^(2)]^(x)) d x is equal to where [.] denotes the greatest integer function

VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -Level - 1
  1. Given f(x) where ={(x|x|,"for" xle -1),([x+1]+[1-x],"for"-1lt x lt...

    Text Solution

    |

  2. If I=underset (0)overset(1) int cos{ 2 "cot"^(-1)sqrt((1-x)/(1+x))}dx ...

    Text Solution

    |

  3. The value of int(-2)^(2)(sin^(2)x)/([(x)/(pi)]+(1)/(2))dx where [.] d...

    Text Solution

    |

  4. Evaluate int-1^1 [x[1+sinpix]+1]dx, [.] is the greatest integer funct...

    Text Solution

    |

  5. Let f(x)=(e^(x)+1)/(e^(x)-1) and int(0)^(1) x^(3) .(e^(x)+1)/(e^(x)-1)...

    Text Solution

    |

  6. Let overset(a)underset(0)int f(x)dx=lambda and overset(a)underset(0)in...

    Text Solution

    |

  7. The value of the integral overset(pi)underset(0)int (sin k x)/(sin x)...

    Text Solution

    |

  8. The value of the integral int0^pi(x^2sinx)/((2x-pi)(1+cos^2x))\ dx

    Text Solution

    |

  9. Let f : R->R be given by f(x) = {|x-[x]|, when [x] is odd and |x-[x...

    Text Solution

    |

  10. If f(x) = sin x+cos x and g(x) = {:{((|x|)/(x),","x ne0),(2,","x=0):} ...

    Text Solution

    |

  11. Let f(x)={(1-|x|","|x|le1),(0","|x|gt1):} and g(x)=f(x-1)"for all" x i...

    Text Solution

    |

  12. Ifint0^1cot^(-1)(1-x+x^2)dx=lambdaint0^1tan^(-1)x dx ,then lambda is e...

    Text Solution

    |

  13. Let d/(dx)F(x)=(e^(sinx))/x . x lt0. If int(1)^(4)(2e^(sinx^(2)))/xdx=...

    Text Solution

    |

  14. Evaluate: int0^x[cost]dt where x in (2npi,(4n+1pi/2),n in N ,a n d[do...

    Text Solution

    |

  15. Ifint0^1(e^t dt)/(t+1)=a ,t h e ne v a l u a t eint(b-1)^b(e^(-t)dt)/(...

    Text Solution

    |

  16. The value of int0^pi (sin(n+1/2)x)/(sin (x/2)) dx is, (a) n in I, n >...

    Text Solution

    |

  17. Consider the integrals I(1)=overset(1)underset(0)inte^(-x)cos^(2)xdx...

    Text Solution

    |

  18. Given overset(2)underset(1)inte^(x^(2))dx=a, the value of overset(e^(4...

    Text Solution

    |

  19. The area bounded by the curve y=[x^2/64+2],y=x-1,y=x-1 and x=0 above t...

    Text Solution

    |

  20. Area enclosed by the curve (y-sin^(- 1)x)^2=x-x^2, is (A) pi/2 sq...

    Text Solution

    |