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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`

Answer

Step by step text solution for 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 by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

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Similar Questions

Explore conceptually related problems

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

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

Knowledge Check

  • int_(0)^(pi) x f (sin x)dx =

    A
    `pi int_(0)^(pi) f (sin x) dx`
    B
    `(pi)/(2) int_(0)^(pi//2) f(sin x)dx`
    C
    `pi int_(0)^(pi//2) f (cos x)dx`
    D
    `pi int_(0)^(pi) f (cos x) dx`

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

    A
    `pi`
    B
    `(pi)/(3)`
    C
    `2pi`
    D
    `(pi)/(2)`

    • Similar Questions

    Explore conceptually related problems

    int_(0)^(pi//2) f(sin 2x) sin x dx= int_(0)^(pi//2) f(sin 2x) cos x dx= sqrt""2 int_(0)^(pi//4) f(cos 2x) cos x dx

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

    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

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