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

Let `f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^4x-3tan^2x` for all `x in (-pi/2,pi/2)` . Then the correct expression (s) is (are) `int_0^(pi/4)xf(x)dx=1/(12)` `int_0^(pi/4)f(x)dx=0` `int_0^(pi/4)xf(x)=1/6` (d) `int_0^(pi/4)f(x)dx=1/(12)`

A

`underset(0)overset(pi//4)intxf(x) dx = 1/12`

B

`underset(0)overset(pi//4)intf(x) dx = 0`

C

`underset(0)overset(pi//4)intxf(x) dx = 1/6`

D

`underset(0)overset(pi//4)intf(x) dx = 1`

Text Solution

Verified by Experts

The correct Answer is:
A, B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 3 Part - II|25 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise High Level Problem|37 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 2 Part - IV|9 Videos

  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

  • DPP

    RESONANCE|Exercise QUESTION|665 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)

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).

int_(0)^( pi)xf(sin x)dx=(pi)/(2)int_(0)^( pi)f(sin x)dx

" (x) "int_(0)^( pi/4)tan xdx

int_{0}^(pi/4)|tan x|dx

int_(0)^(pi//4) tan x dx

int_0^(pi/4) (tanx-x)tan^2xdx

(i) int_0^(pi//4) tan x dx (ii) int_(pi//4)^(pi//2) cot x dx

RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I
  1. If alpha = int(0)^(1)e^(9x+3tan^(-1)x)) ((12+9x^(2))/(1+x^(2)))dx wher...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. Let f'(x) = (192x^(2))/(2+sin^(4)pix) for all x in R with f(1/2) = 0. ...

    Text Solution

    |

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

    Text Solution

    |

  6. Let F:R- R be a thrice differentiable function. Suppose that F(1)=0,F(...

    Text Solution

    |

  7. Let F : R rarr R be a thrice differentiable function, Supose that F(...

    Text Solution

    |

  8. Let F(x) = int(x)^(x^(2)+(pi)/(6))2cos^(2)t dt for all x in R and f: [...

    Text Solution

    |

  9. The total number of distinct x in (0,1] for which int(0)^(x)(t^(2))/...

    Text Solution

    |

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

    Text Solution

    |

  11. Area of region {(x,y) in R^(2): y ge sqrt(|x+3|,)5y le x + 9 le 15}

    Text Solution

    |

  12. Let f(x) = lim(nrarroo) ((n^(n)(x+n)(x+n/2)"......."(x+n/n))/(n!( x^(...

    Text Solution

    |

  13. Let f: Rvec(0,1) be a continuous function. Then, which of the followin...

    Text Solution

    |

  14. Let f : R rarr R be a defferentiable function such that f(0) = 0 , f(p...

    Text Solution

    |

  15. If Isum(k=1)^(98)intk^(k+1)(k+1)/(x(x+1))dx ,t h e n: I<(49)/(50) ...

    Text Solution

    |

  16. If the line x = alpha divides the area of region R = {(x,y) in R^(2) :...

    Text Solution

    |

  17. If g(x)=int(sinx)^("sin"(2x))sin^(-1)(t)dt ,t h e n : g^(prime)(pi/2)...

    Text Solution

    |

  18. For each positive integer n, let y(n) = 1/n ((n+1)(n+2) "……"(n+n))^...

    Text Solution

    |

  19. A farmer F1 has a land in the shape of a triangle with vertices at ...

    Text Solution

    |

  20. The value of the intetgral int(0)^(1//2)(1+sqrt(3))/(((x+1)^(2)(1-x)^...

    Text Solution

    |