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int0^(2pi)(sin2x)dx...

`int_0^(2pi)(sin2x)dx`

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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//2) (sin 2x)/(a^2 + b^2 sin^2 x) dx =

    A
    `0`
    B
    `pi//4`
    C
    `1/(b^2) "log" ((a^2 + b^2)/(a^2)) `
    D
    `1/(b^2)"log" (a^2 + b^2)`

  • If I=int_(0)^(2pi) sin^(2) x" dx" , then

    A
    `I=4overset(pi)underset(0)int sin^(2)x" dx"=4overset(pi//2)underset(0)int sin^(2)x" dx"`
    B
    `I=overset(pi//2)underset(0)intcos^(2)x" dx"`
    C
    `I=8overset(pi//4)underset(0)int sin^(2)x" dx"`
    D
    none of these

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

    Evaluate each of the following integral: int_0^(pi//2)sin^2x\ dx

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