Home
Class 12
MATHS
If f (x+y) =f (x) f(y) for all x,y and ...

If `f (x+y) =f (x) f(y)` for all x,y and `f (0) ne 0, and F (x) =(f(x))/(1+(f (x))^(2))` then:

A

`int _(-2010) ^(2011) F (x)dx =int _(0) ^(2011) F (x)dx `

B

`int _(-2010) ^(2011) F (x)dx =int _(0) ^(2011) F (x)dx =int _(0)^(2011)F (x) dx`

C

`int _(-2010) ^(2011) F (x) dx =0`

D

`int _(-2010) ^(2010) (2F(-x) -F(x)) dx =e int _(0)^(2010) F (x) dx `

Text Solution

Verified by Experts

The correct Answer is:
B, D
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE AND DEFINITE INTEGRATION

    VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|17 Videos

  • INDEFINITE AND DEFINITE INTEGRATION

    VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|29 Videos

  • INDEFINITE AND DEFINITE INTEGRATION

    VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|29 Videos

  • HYPERBOLA

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

  • INVERSE TRIGONOMETRIC FUNTIONS

    VIKAS GUPTA (BLACK BOOK)|Exercise Exercise-5 : Subjective Type Problems|6 Videos

Similar Questions

Explore conceptually related problems

If f(x+y)=f(x).f(y) for all real x,y and f(0)!=0, then the function g(x)=(f(x))/(1+{f(x)}^(2)) is:

If f(x) + f(y) = f((x+y)/(1-xy)) for all x, y in R (xy ne 1) and lim_(x rarr 0) (f(x))/(x) = 2 , then

f(x+y)=f(x)*f(y) for all x,y anf f(5)=2,f'(0)=3 then f(5) will be

Let a real valued function f satisfy f(x+y)=f(x)f(y)AA x,y in R and f(0)!=0 Then g(x)=(f(x))/(1+[f(x)]^(2)) is

If f(x+y)=f(x)f(y) for all real x and y, f(6)=3 and f'(0)=10 , then f'(6) is

If f((x)/(y))=(f(x))/(f(y)) for all x, y in R, y ne 0 and f'(x) exists for all x, f(2) = 4. Then, f(5) is

If f(x+y)=f(x)*f(y) for all real x,y and f(0)!=0, then prove that the function g(x)=(f(x))/(1+{f(x)}^(2)) is an even function.

If f(x-y), f(x) f(y), and f(x+y) are in A.P. for all x, y, and f(0) ne 0, then

VIKAS GUPTA (BLACK BOOK)-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
  1. int (dx)/((1+sqrtx)^(8))=-(1)/(3(1+sqrtx)^(k(2)))+ (2)/(7(1+sqrtx)^(k(...

    Text Solution

    |

  2. If int (-alpha) ^(alpha ) (e ^(x) + cos x ln (x + sqrt(1+x ^(2))))dx g...

    Text Solution

    |

  3. "I f"intsqrt(x/(a^3-x^3))dx=d/bsin^(- 1)((x^(3/2))/(a^(3/2)))+C (wher...

    Text Solution

    |

  4. Let int x sinx sec^3x dx = 1/2(x.f(x) - g(x)) + k, then

    Text Solution

    |

  5. If int(sin3theta+sintheta)costhetae^sinthetadtheta=(Asin^3theta+Bcos^2...

    Text Solution

    |

  6. For a gt 0, if I = int sqrt((x)/(a ^(3) -x ^(3)))dx = A sin ^(-1) ((x ...

    Text Solution

    |

  7. If f (theta ) = lim (x to oo) sum ( r =o) ^(n theta) (2r)/(n sqrt((3 t...

    Text Solution

    |

  8. If f (x+y) =f (x) f(y) for all x,y and f (0) ne 0, and F (x) =(f(x))/...

    Text Solution

    |

  9. Let J=int (-1) ^(2) (cot ^(-1) ""(1)/(x )+ cot ^(-1) x ) dx, K =int (-...

    Text Solution

    |

  10. Which of the following function (s) is/are even ?

    Text Solution

    |

  11. Let lim(x->oo) sqrt((x-cos^2x)/(x+sinx)) and I2 = lim(h->0^+) int(-1)^...

    Text Solution

    |

  12. For a gt 0, if I = int sqrt((x )/(a ^(3) -x ^(3)))dx =A sin ^(-1) ((x...

    Text Solution

    |

  13. If int (dx)/(1- sin ^(4)x )= a tan x +b tan ^(-1) (c tan x )+ D, then...

    Text Solution

    |

  14. The value of definite integral: int(-2014)^(2014)(dx)/(1+sin^(2015)x+s...

    Text Solution

    |

  15. Let L= underset(nrarr infty)(lim)int(a)^(infty)(n dx)/(1+n^(2)x^(2)), ...

    Text Solution

    |

  16. Let I =int (0)^(1 ) sqrt((1+sqrtx)/(1-sqrtx))dx and J = int (0)^(1 ) s...

    Text Solution

    |