Home
Class 12
MATHS
Let f (x) = 7 tan ^(8) x + 7 tan ^(6) x ...

Let `f (x) = 7 tan ^(8) x + 7 tan ^(6) x - 3 tan ^(4) x - 3 tan ^(2) x ` for all `x in (-(pi)/(2), (pi)/(2)).` Then the correct expression(s) is (are).

A

`int _( 0 ) ^(pi//4) x f ( x ) dx= (1)/(12)`

B

`int _(0) ^(pi//4) f (x) dx =0`

C

`int _(0) ^(pi//4) xf (x) dx = 1/6`

D

` int_(0) ^(pi//4)f (x) dx =1`

Text Solution

Verified by Experts

The correct Answer is:
A, B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    MOTION|Exercise EXERCISE -4 LEVEL-I|15 Videos
  • CONTINUITY

    MOTION|Exercise EXERCISE - 4 (LEVEL -II) (PREVIOUS YEAR JEE ADVANCED)|5 Videos
  • DETERMINANTS

    MOTION|Exercise EXERCISE-4 (LEVEL-II)|6 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=7 tan^(8) x +7 tan^(4) x-3 tan^(2)x for all x in(-(pi)/(2),(pi)/(2)) . Then the correct expression (s) is are

Let f(x)=7tan^(8)x+7tan^(6)x-3tan^(4)x-3tan^(2)x for all x in(-(pi)/(2),(pi)/(2))* Then the correct expression (s) is (are) (a) int_(0)^((pi)/(4))xf(x)dx=(1)/(12) (b) int_(0)^((pi)/(4))f(x)dx=0( c) int_(0)^((1)/(4))xf(x)=(1)/(6)(d)int_(0)^((pi)/(4))f(x)dx=(1)/(12)

If f(x) = tanx-tan ^(3) x + tan^(5) x - tan ^(7) x + ... infty for olt x lt pi/4 , "than" int_(0)^(pi//4) f (x) dx=

If f (x) = sqrt(cos ec ^(2) x - 2 sin x cos x - (1)/(tan ^(2) x )) x in ((7pi)/(4), 2pi ) then f' ((11 pi)/(6))=

The value lim_(x to tan^(-1) 3) (tan^6 x- 2tan^5 x - 3tan^4 x)/(tan^2 x -4 tan x+3)

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:

If f'(x) = tan^(-1)(Sec x + tan x), x in (-pi/2 , pi/2) and f(0) = 0 then the value of f(1) is

Let f(x)=7Tan^(8)x+7Tan^(6)x-4tan^(5)x-4tan^(3)x and int f(x)dx=g(x) where g(0)=0 then the value of g((pi)/(4))=

If f(x)=tan^(2)((pi x)/6) ,then f'(2)

MOTION-DEFINITE INTEGRATION -EXERCISE -4 LEVEL-II
  1. T h ev a l u eofint(sqrt(1n2))^(sqrt(1n3))(xsinx^2)/(sinx^2+sin(1n6-x^...

    Text Solution

    |

  2. Let f:[1,oo] be a differentiable function such that f(1)=2. If int1...

    Text Solution

    |

  3. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

    Text Solution

    |

  4. Let f:[1/2,1]vecR (the set of all real numbers) be a positive, non-con...

    Text Solution

    |

  5. Find a for which lim(n->oo) (1^a+2^a+3^a+...+n^a)/((n+1)^(a-1)[(na+1)+...

    Text Solution

    |

  6. Let f:(0,oo)vecR be given by f(x)=int(1/x)^x(e^(-(t+1/t))dt)/t , then ...

    Text Solution

    |

  7. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

    Text Solution

    |

  8. The integral overset(pi//2)underset(pi//4)int (2 cosecx)^(17)dx is equ...

    Text Solution

    |

  9. Let f: RvecR be a function defined by f(x)={[x],xlt=2 0,x >2 where [...

    Text Solution

    |

  10. If alpha=int0^1(e^9x+3tan^((-1)x))((12+9x^2)/(1+x^2))dxw h e r etan^(-...

    Text Solution

    |

  11. Let f: RvecR be a continuous odd function, which vanishes exactly at o...

    Text Solution

    |

  12. Let f (x) = 7 tan ^(8) x + 7 tan ^(6) x - 3 tan ^(4) x - 3 tan ^(2) x ...

    Text Solution

    |

  13. Let f^(prime)(x)=(192 x^3)/(2+sin^4pix)fora l lx in Rw i t hf(1/2)=0....

    Text Solution

    |

  14. Let F : R to R be a thrice differentiable function . Suppose that F(...

    Text Solution

    |

  15. Let F : R to R be a thrice differentiable function . Suppose that F(...

    Text Solution

    |

  16. The total number of distincts x in [0,1] for which int(0)^(x) (t^(2))...

    Text Solution

    |

  17. Let f(x)=lim(n->oo)((n^n(x+n)(x+n/2)....(x+n/n))/(n!(x^2+n^2)(x^2+n^2/...

    Text Solution

    |

  18. Let f: R -> R be a differentiable function such that f(0)=0, f((pi/2))...

    Text Solution

    |

  19. For each positive integer n, let jy(n) =1/n ((n +1) (n +2) …(n +n) )...

    Text Solution

    |

  20. The value of the integral int0^(1/2)(1+sqrt(3))/(((x+1)^2(1-x)^6)^(...

    Text Solution

    |