Home
Class 12
MATHS
If [.] stands for the greatest integer f...

If [.] stands for the greatest integer function, then `int_(1)^(2) [3x]dx` is equal to

A

3

B

4

C

5

D

6

Text Solution

Verified by Experts

The correct Answer is:
B
We observe that when `x in [1,2], 3x in [3,6]`.
`:.overset(2)underset(1)int [3x]dx=overset(4//3)underset(1)int[3x]dx+overset(5//3)underset(4//3)int[3x]dx+overset(6//3)underset(5//3)int[3x]dx`
`rArr overset(2)underset(1)int [3x]dx=overset(4//3)underset(1)int 3dx+overset(5//3)underset(4//3)int 4dx+overset(6//3)underset(5//3)int 5dx`
`rArr overset(2)underset(2)int [3x]dx=3((4)/(3)-1)+4((5)/(3)-(4)/(3))+5((6)/(3)-(6)/(3))=1+(4)/(3)+(5)/(3)=4`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Section I - Solved Mcqs|145 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|12 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA|Exercise Exercise|86 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

Let f : R to R is a function defined as f(x) where = {(|x-[x]| ,:[x] "is odd"),(|x - [x + 1]| ,:[x] "is even"):} [.] denotes the greatest integer function, then int_(-2)^(4) dx is equal to

If [x] stands for the greatest integer function, the value of int_(4)^(10)([x^(2)])/([x^(2)-28x+196]+[x^(2)])dx , is

Consider the functions f(x) = g(x) and g(x) = [1/x] Where [.] is the greatest integer function. What is int_(1/3)^(1/2) g(x)dx equal to ?

If [:] denotes the greatest integer function, then find the value of int_(1)^(2)[3x]dx

Consider the functions f(x) = g(x) and g(x) = [1/x] Where [.] is the greatest integer function. What is int_(1/3)^(1) f(x) dx equal to ?

If int_(-a)^(a) ( | x | + |x-2 |) dx =22 , ( a gt 2) and [x] denotes the greatest integer le x , then int_(-a)^(a) (x +[x])dx is equal to ______

f(x)={3[x]-5(|x|)/(x),x!=0 and 2,x=0 where [.] denotes the greatest integer function,then int_(-(3)/(2))^(2)f(x)dx equals

If [dot] denotes the greatest integer function, then find the value of int_1^2[3x]dx

OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Chapter Test 2
  1. If [.] stands for the greatest integer function, then int(1)^(2) [3x]...

    Text Solution

    |

  2. The integral int(0)^(r pi) sin^(2x)x dx is equal to

    Text Solution

    |

  3. The value of the integral int(0)^(2)x[x]dx

    Text Solution

    |

  4. The value of integral sum (k=1)^(n) int (0)^(1) f(k - 1+x) dx is

    Text Solution

    |

  5. Let f(x) be a funntion satifying f'(x)=f(x) with f(0)=1 and g(x) be th...

    Text Solution

    |

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

    Text Solution

    |

  7. The value of int(a)^(a+(pi//2))(sin^(4)x+cos^(4)x)dx is

    Text Solution

    |

  8. The vaue of int(-1)^(2) (|x|)/(x)dx is

    Text Solution

    |

  9. The value of int0^1 (x^(3))/(1+x^(8))dx is

    Text Solution

    |

  10. The value of int(0)^(3) xsqrt(1+x)dx, is

    Text Solution

    |

  11. The value of the integral int(0)^(1) log sin ((pix)/(2))dx is

    Text Solution

    |

  12. The value of the integral int(0)^(pi)x log sin x dx is

    Text Solution

    |

  13. If I(1)=int(0)^(oo) (dx)/(1+x^(4))dx and I(2)underset(0)overset(oo)in...

    Text Solution

    |

  14. If f(x)={{:(x,"for " x lt 1),(x-1,"for " x ge1):},"then" int(0)^(2) x...

    Text Solution

    |

  15. The value of the integral int(0)^(2) (1)/((x^(2)+1)^(3//2))dx is

    Text Solution

    |

  16. If int(0)^(2a) f(x)dx=int(0)^(2a) f(x)dx, then

    Text Solution

    |

  17. If int(0)^(36) (1)/(2x+9)dx =log k, is equal to

    Text Solution

    |

  18. The value of the integral int(0)^(pi//2) sin^(6) x dx, is

    Text Solution

    |

  19. If int(0)^(oo) e^(-x^(2))dx=sqrt((pi)/(2))"then"int(0)^(oo) e^(-ax^(2)...

    Text Solution

    |

  20. The value of the integral int 0^oo 1/(1+x^4)dx is

    Text Solution

    |

  21. If int(pi//2)^(x) sqrt(3-2sin^(2)u) dx+int(dx)^(dy) equal pi//2

    Text Solution

    |