Home
Class 12
MATHS
The value of int(-2)^1[x[1+cos((pix)/2)]...

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

A

`1`

B

`1//2`

C

`2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C

From graph `int_(-2)^(1)[x[1+"cos"(pix)/2]+1]dx`
`=int_(-2)^(-1) [x[1+(-1)]+1]dx+int_(-1)^(1)[x[10]+1]dx`
`=(x)_(-2)^(-1)+int_(-1)^(1)[x+1]dx`
`=(-1-(-2))+int_(-1)^(0)0dx+int_(0)^(1)1dx=2`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise MCQ_TYPE|27 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise LC_TYPE|31 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CAE_TYPE|88 Videos

  • CURVE TRACING

    CENGAGE PUBLICATION|Exercise EXERCISES|24 Videos

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

The value of int_(-2)^2 (sin^2x)/([x/pi]+1/2) dx where [x] denotes the greatest integer lex is

lim_(xrarr1([x]+[x]) , (where [.] denotes the greatest integer function )

int_(-1)^2[([x])/(1+x^2)]dx ,w h e r e[dot] denotes the greater integer function, is equal to (a) -2 (b) -1 (c) 0 (d) none of these

Evaluate: int_(-pi/2)^(2pi)[cot^(-1)x]dx , where [dot] denotes the greatest integer function

Evaluate: int_(-pi/2)^(2pi)[cot^(-1)x]dx , where [dot] denotes the greatest integer function

The period of the function f(x)=[6x+7]+cospix-6x , where [dot] denotes the greatest integer function is: (a)3 (b) 2 pi (c) 2 (d) none of these

Solve [cot^(-1) x] + [cos^(-1) x] =0 , where [.] denotes the greatest integer function

Evaluate: int_(-5)^5x^2[x+1/2]dx(w h e r e[dot] denotes the greatest integer function).

int_(pi/2)^(3pi/2) [2sinx]dx is equal to [x] denotes the greatest integer function

lim_(xto1) (xsin(x-[x]))/(x-1) , where [.] denotes the greatest integer function, is equal to

CENGAGE PUBLICATION-DEFINITE INTEGRATION -SCQ_TYPE
  1. int(3)^(10)[log[x]]dx is equal to (where [.] represents the greatest i...

    Text Solution

    |

  2. int(-1)^2[([x])/(1+x^2)]dx ,w h e r e[dot] denotes the greater integer...

    Text Solution

    |

  3. The value of int(-2)^1[x[1+cos((pix)/2)]+1]dx , where [.] denotes the...

    Text Solution

    |

  4. The value of int0^(2pi)[2sinx]dx ,w h e r e[dot] represents the greate...

    Text Solution

    |

  5. I1=int0^(pi/2)(sinx-cosx)/(1+sinxcosx)dx ,I2=int0^(2pi)cos^6xdx ,I3=in...

    Text Solution

    |

  6. Given int(0)^(pi//2)(dx)/(1+sinx+cosx)=A. Then the value of the defini...

    Text Solution

    |

  7. "I f"I1=int(-100)^(101)(dx)/((5+2x-2x^2)(1+e^(2-4x))) "and"I2=int(-10...

    Text Solution

    |

  8. Find the value of int(0)^(oo)(xdx)/((1+x)(1+x^(2))) equals to

    Text Solution

    |

  9. Q. int0^pie^(cos^2x)( cos^3(2n+1) x dx, n in I

    Text Solution

    |

  10. Let f be a positive function. Let I1=int(1-k)^k xf([x(1-x)]dx , I2=i...

    Text Solution

    |

  11. If f(x) =(e^x)/(1+e^x), I1=int(f(-a))^(f(a)) xg(x(1-x))dx, and I2=int(...

    Text Solution

    |

  12. The value of int1^((1+sqrt(5))/2)(x^2+1)/(x^4-x^2+1)log(1+x-1/x)dx is...

    Text Solution

    |

  13. The value of the definite integral int0^(pi/2)sqrt(tanx)dx is (a) s...

    Text Solution

    |

  14. f(x)>0AAx in R and is bounded. If lim(n->oo)[int0^a(f(x)dx)/(f(x)+f(a...

    Text Solution

    |

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

    Text Solution

    |

  16. The value of the definite integral int(-1)^(1)(1+x)^(1//2)(1-x)^(3//2)...

    Text Solution

    |

  17. T h ev a l u eoft h ein t egr a lint(-(3pi)/4)^((5pi)/4)((sinx+cosx)/(...

    Text Solution

    |

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

    Text Solution

    |

  19. If I1=int0^(pi//2)(cos^2x)/(1+cos^2x)dx , I2=int0^(pi//2)(sin^2x)/(1+s...

    Text Solution

    |

  20. Evaluate : int0^(pi/2)(xsinxcosx)/(sin^4x+cos^4x)\ dx

    Text Solution

    |