Home
Class 12
MATHS
If f(x)=(1+ tan x) [1+ tan(pi/4 - x)] an...

If `f(x)=(1+ tan x) [1+ tan(pi/4 - x)]` and `g(x)` is a function with domain R, then `int_(0)^(1) x^(3) g o f (x) dx=`

A

`1/2 g(pi/4)`

B

`1/4 g(2)`

C

`1/4g(1)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|151 Videos

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise Examples|8 Videos

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise EXERCISE - I|67 Videos

  • COMPLEX NUMBERS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|93 Videos

  • DEMOIVRE'S THEOREM

    AAKASH SERIES|Exercise PRACTICE EXERCISE|64 Videos

Similar Questions

Explore conceptually related problems

int_(0)^(pi//3) |tan x - 1|dx=

If (d)/(dx) f(x) = g(x) then int_(a)^(b) f(x) g(x) dx=

int_(0)^(pi//2)(dx)/(1+tan^(3)x)=

If int_(0)^(pi) f(tan x) dx= lambda then int_(0)^(2pi) f(tan x) dx=

If f(x)=sin x + cos x, g(x)=x^(2)-1 , then g(f(x)) is invertible in the domain

If f(x)=sin x + cos x, g(x)=x^(2)-1 , then g(f(x)) is invertible in the domain

The domain of f(x)=Tan^(-1)5x is

If f(x)=sin(sinx) an f f'(x) +tan xf'(x)+g(x)=0 , then g(x) is :

AAKASH SERIES-DEFINITE INTEGRALS-EXERCISE - II
  1. Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1andg(x) be a f...

    Text Solution

    |

  2. Let F(x)= f(x) + f(1/x), where f(x)= int(1)^(x) (ln t)/(1+t)dt, then F...

    Text Solution

    |

  3. If f(x)=(1+ tan x) [1+ tan(pi/4 - x)] and g(x) is a function with doma...

    Text Solution

    |

  4. y= int(x)^(x^(2)) sqrt(5-t^(2))dt then the value of (dy)/(dx) at x= sq...

    Text Solution

    |

  5. If int(e)^(x) t f(t)dt= sin x - x cos x - (x^(2))/(2) for all x in R -...

    Text Solution

    |

  6. If int(0)^(b-c) f(x+c) dx = k int(b)^(c) f (x) dx then k=

    Text Solution

    |

  7. If f is every where continuous function then 1/c int(ac)^(bc) f(x/c) d...

    Text Solution

    |

  8. If int(0)^(pi) f(tan x) dx= lambda then int(0)^(2pi) f(tan x) dx=

    Text Solution

    |

  9. int(0)^(2) (2x-2)/(2x-x^(2))dx=

    Text Solution

    |

  10. Evaluate (i) int(0)^(pi/2) (sin^(2)x)/(sin x + cos x ) dx

    Text Solution

    |

  11. int(0)^(1) Tan^(-1) ((2x-1)/(1+x-x^(2)))dx=

    Text Solution

    |

  12. int(0)^(oo) (ln x)/(x^(2)+a^(2))dx=

    Text Solution

    |

  13. int(0)^(pi//2) ln (tan x+ cot x)dx=

    Text Solution

    |

  14. Evaluate the integral underset(0)overset(1)int (log(1+x))/(1+x^(2))d...

    Text Solution

    |

  15. int(0)^(2pi) ln (1+Cos x) dx=

    Text Solution

    |

  16. int(0)^(pi//2) (sin 8x.log(cot x))/(cos 2 x)dx=

    Text Solution

    |

  17. int(0)^(4014) (2^(x))/(2^(x) +2^(4041-x))dx=

    Text Solution

    |

  18. int(0)^(pi//2) (1)/(1+e^(sqrt(2)sin(x-pi//4)))dx=

    Text Solution

    |

  19. If f(y)=e^(y),g(y)=y:ygt0andF(t)=int(0)^(t)f(t-y)g(y)dy, then

    Text Solution

    |

  20. int(0)^(2pi)(1)/(e^(sin x) +1) dx=

    Text Solution

    |