Home
Class 12
MATHS
Show that (i) int(0)^(pi//2)f(sinx) d ...

Show that (i) `int_(0)^(pi//2)f(sinx) d x=int_(0)^(pi//2)f(cos x) d x` (ii) `int_(0)^(pi//2)f(tan x) d x=int_(0)^(pi//2)f(cot x) d x` (iii) `int_(0)^(pi//2)f(sin 2 x) sin xd x = int_(o)^(pi//2)f(sin 2x).cosx d x`

Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 1|15 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 2|14 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

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

Show that: int_(0)^( pi/2)f(sin2x)sin xdx=sqrt(2)int_(0)^( pi/4)f(cos2x)cos xdx

If int_(0)^(pi)x f(sin x) dx = a int_(0)^(pi)f (sin x) dx , then a =

Prove the equality int_(0)^(pi) f (sin x) dx = 2 int_(0)^(pi//2) f (sin x) dx

Evaluate (i) int_(0)^(pi//2)(d x)/(1+sqrt(tan x)) (ii) int_(0)^(pi//2) log (tan x ) d x (iii) int_(0)^(pi//4) log (1+tan x ) d x (iv) int_(0)^(pi//2)(sin x- cos x)/(1+ sin x cos x)d x

=I^(int_(0)^( pi/2))(x)/(sin x+cos x)

underset is If int_(0)^( pi)xf(sin x)dx=A int_(0)^((pi)/(2))f(sin x)dx, then A

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Show that (i) int(0)^(pi//2)f(sinx) d x=int(0)^(pi//2)f(cos x) d x ...

    Text Solution

    |

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

    Text Solution

    |

  3. The total number for distinct x epsilon[0,1] for which int(0)^(x)(t^(2...

    Text Solution

    |

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

    Text Solution

    |

  5. Let f prime(x)=(192x^3)/(2+sin^4 pix) for all x in RR with f(1/2)=0. I...

    Text Solution

    |

  6. The option(s) with the values of aa n dL that satisfy the following eq...

    Text Solution

    |

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

    Text Solution

    |

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

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

    Text Solution

    |

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

    Text Solution

    |

  13. Match the conditions/ expressions in Column I with statement in Column...

    Text Solution

    |

  14. Match List I with List II and select the correct answer using codes gi...

    Text Solution

    |

  15. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dxi s

    Text Solution

    |

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

    Text Solution

    |

  17. The value of int(sqrt(ln2))^(sqrt(ln3)) (xsinx^2)/(sinx^2+sin(ln6-x^2)...

    Text Solution

    |

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

    Text Solution

    |

  19. The value of int(0)^(1) (x^(4)(1-x)^(4))/(1+x^(2)) dx is (are)

    Text Solution

    |

  20. For a in R ( the set of all real number) , a ne -1, lim(n to oo)((1^...

    Text Solution

    |

  21. Consider the statements : P : There exists some x IR such that f(x)...

    Text Solution

    |