Home
Class 12
MATHS
Evaluate: int0^x[cost]dtw h e r en in (2...

Evaluate: `int_0^x[cost]dtw h e r en in (2npi,(4n+1pi/2),n in N ,a n d[dot]` denotes the greatest integer function.

Text Solution

Verified by Experts

Let
`I=int_(0)^(x)[cos t] dt`
`=int_(0)^(2npi)[cost]dt+int_(2pi)^(x)[cost]dt`
`=nint_(0)^(2pi)[cost]dt+int_(2npi)^(x)[cost]dt`
`=-npi+int_(2npi)^(x)0 dt`
`=-npi`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise SOLVED EXAMPLE_TYPE|20 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

Evaluate: int_0^x[cost]dt where x in (2npi,(4n+1pi/2),n in N ,a n d[dot] denotes the greatest integer function.

int_0^x[cost]dt ,w h e r ex in (2npi,2npi+pi/2),n in N ,a n d[dot] denotes the greatest integer function . then the value of f(1/pi) is

Evaluate: int_0^(2pi)[sinx]dx ,where [dot] denotes the greatest integer function.

Evaluate: int_0^((5pi)/(12))[tanx]dx , where [dot] 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).

Evaluate: int_0^2[x^2-x+1]dx ,w h e r e[dot] denotos the greatest integer function.

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

Evaluate: int_1^(e^6)[(logx)/3]dx ,w h e r e[dot] denotes the greatest integer function.

If -int_0^(2pi) [sinx+cosx]dx =Api and [x] denotes the greatest integer function then A is equal to

CENGAGE PUBLICATION-DEFINITE INTEGRATION -JEE ADVANCED
  1. Evaluate: int0^x[cost]dtw h e r en in (2npi,(4n+1pi/2),n in N ,a n d[...

    Text Solution

    |

  2. Let f be a non-negative function defined on the interval [0,1]. If int...

    Text Solution

    |

  3. The value of int0^1(x^4(1-x)^4)/(1+x^2)dxi s//a r e (22)/7-pi (b) 2/...

    Text Solution

    |

  4. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  5. The value of int(in2)^sqrt(in3) (xsinx^2)/(sinx^2+sin(In6-x^2)dx is

    Text Solution

    |

  6. Let f:[-1,2]vec[0,oo) be a continuous function such that f(x)=f(1-x)fo...

    Text Solution

    |

  7. Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-cons...

    Text Solution

    |

  8. Let f : [0,2] rarr R be a function which is continuous on [0 , 2] and ...

    Text Solution

    |

  9. int((pi)/4)^((pi)/2)(2cosecx)^17 dx

    Text Solution

    |

  10. Let f prime(x)=(192x^3)/(2+sin^4 pix) for all x in RR with f(1/2)=0. I...

    Text Solution

    |

  11. The value of int(-pi/2)^(pi/2) (x^2cosx)/(1+e^x) dx is equal to

    Text Solution

    |

  12. If In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

    Text Solution

    |

  13. about to only mathematics

    Text Solution

    |

  14. Let S be the area of the region enclosed by y=e^(-x^(2)),y=0, x=0 and ...

    Text Solution

    |

  15. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...

    Text Solution

    |

  16. Let f:[a,b]rarr[1,infty) be a continuous function and lt g: RrarrR be ...

    Text Solution

    |

  17. Let f:(0,oo)rarrRR be given by f(x)=oversetxunderset(1/x)inte^((t+1/...

    Text Solution

    |

  18. The option(s) with the values of a and L that satisfy the following eq...

    Text Solution

    |

  19. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2, pi/2). T...

    Text Solution

    |

  20. find the period of sin(x/2)-cos(x/3) is

    Text Solution

    |

  21. Let f: Rto(0,1) be a continuous function. Then, which of the following...

    Text Solution

    |