Home
Class 12
MATHS
If int (cosec ^(2)x-2010)/(cos ^(2010)x)...

If `int (cosec ^(2)x-2010)/(cos ^(2010)x)dx = =(f (x))/((g (x ))^(2010))+C,` where `f ((pi)/(4))=1,` then the number of solution of the equation `(f(x))/(g (x))={x}` in `[0,2pi]` is/are: (where {.} represents fractional part function)

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE AND DEFINITE INTEGRATION

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|16 Videos

  • INDEFINITE AND DEFINITE INTEGRATION

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|14 Videos

  • HYPERBOLA

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-4 : Subjective Type Problems|3 Videos

  • INVERSE TRIGONOMETRIC FUNTIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-5 : Subjective Type Problems|5 Videos

Similar Questions

Explore conceptually related problems

If int(sec^(2)x-2010)/(sin^(2010)x)dx=(P(x))/(sin^(2010) x)+C , then value of P((pi)/(3)) is

The number of solutions of the equation cos ^(-1)((1-x ^(2) -2x)/((x+1) ^(2)))=pi (1- {x}, for x in[0,76] is equal to (where {.} denote fraction part function)

If domain of f(x) is (-oo,0) , then domain of f(6{x}^2-5(x)+ 1) is (where {.} represents fractional part function)

The period of the function f(x)=cos2pi{2x}+ sin2 pi {2x} , is ( where {x} denotes the functional part of x)

The period of the function f(x)=cos2pi{2x}-sin2 pi {2x} , is ( where {x} denotes the functional part of x)

If f(x)={x}+{2x} and g(x)=[x]. The number of solutions of f(x)=g(x), where {.} and [x] are respectively the fractional part and greatest functions, is

Let f (x) = int x ^(2) cos ^(2)x (2x + 6 tan x - 2x tan ^(2) x ) dx and f (x) passes through the point (pi, 0) The number of solution (s) of the equation f (x) =x ^(3) in [0, 2pi] be:

The no. of solutions of the equation a^(f(x)) + g(x)=0 where a>0 , and g(x) has minimum value of 1/2 is :-

The range of the function f(x)=cosec^(-1)[sinx] " in " [0,2pi] , where [*] denotes the greatest integer function , is

The function f(x)= cos ""(x)/(2)+{x} , where {x}= the fractional part of x , is a

VIKAS GUPTA (BLACK BOOK) ENGLISH-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. If int (cosec ^(2)x-2010)/(cos ^(2010)x)dx = =(f (x))/((g (x ))^(2010)...

    Text Solution

    |

  2. int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k (1)) ( sqrt(1...

    Text Solution

    |

  3. If int (0)^(oo) (x ^(3))/((a ^(2)+ x ^(2)))dx = (1)/(ka ^(6)), then fi...

    Text Solution

    |

  4. Let f (x) = x cos x, x in [(3pi)/(2), 2pi] and g (x) be its inverse. ...

    Text Solution

    |

  5. If int (x ^(6) +x ^(4)+x^(2)) sqrt(2x ^(4) +3x ^(2)+6) dx = ((ax ^(6) ...

    Text Solution

    |

  6. If the value of the definite integral int ^(-1) ^(1) cos ^(-1) ((1)/(s...

    Text Solution

    |

  7. The value of int (tan x )/(tan ^(2) x + tan x+1)dx =x -(2)/(sqrtA) tan...

    Text Solution

    |

  8. Let int (0)^(1) (4x ^(3) (1+(x ^(4)) ^(2010)))/((1+x^(4))^(2012))dx = ...

    Text Solution

    |

  9. Let int ( 1) ^(sqrt5)(x ^(2x ^(2)+1) +ln "("x ^(2x ^(2x ^(2)+1))")")dx...

    Text Solution

    |

  10. If int (dx )/(cos ^(3) x-sin ^(3))=A tan ^(-1) (f (x)) +bln |(sqrt2+f ...

    Text Solution

    |

  11. Find the value of |a| for which the area of triangle included between ...

    Text Solution

    |

  12. Let I = int (0) ^(pi) x ^(6) (pi-x) ^(8)dx, then (pi ^(15))/((""^(15) ...

    Text Solution

    |

  13. If I = int (0) ^(100) (sqrtx)dx, then the value of (9I)/(155) is:

    Text Solution

    |

  14. Let I(n) = int (0)^(pi) (sin (n + (1)/(2))x )/(sin ((x)/(2)))dx where ...

    Text Solution

    |

  15. If M be the maximum value of 72 int (0) ^(y) sqrt(x ^(4) +(y-y^(2))^(2...

    Text Solution

    |

  16. Find the number points where f (theta) = int (-1)^(1) (sin theta dx )/...

    Text Solution

    |

  17. underset(nrarroo)lim[(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)...

    Text Solution

    |

  18. The maximum value of int (-pi//2) ^(2pi//2) sin x. f (x) dx, subject t...

    Text Solution

    |

  19. Given a function g, continous everywhere such that g (1)=5 and int (0)...

    Text Solution

    |

  20. If f (n)= 1/pi int (0) ^(pi//2) (sin ^(2) (n theta) d theta)/(sin ^(2)...

    Text Solution

    |

  21. Let f (2-x) =f (2+xand f (4-x )= f (4+x). Function f (x) satisfies int...

    Text Solution

    |