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int0^(pi/2) sqrt(sinx)/(sqrt(sinx)+sqrt(...

`int_0^(pi/2) sqrt(sinx)/(sqrt(sinx)+sqrt(cosx))dx`

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STATEMENT-1 : int_(-3)^(3)|x|dx=9 STATEMENT-2 : int_(0)^(1)tan^(-1)xdx=(pi)/(4)-lnsqrt(2) STATEMENT-3 : int_(0)^(pi//2)(sqrt(cosx))/(sqrt(sinx)+sqrt(cosx))dx=(pi)/(4)

Evaluate int_0^(pi/2) sqrt(cosx)/(sqrt(cosx)+sqrt(sinx))dx

Knowledge Check

  • int_(pi//6)^(pi//3)(sqrt(sinx))/(sqrt(sinx)+sqrt(cosx))dx=(k)/(4) , then the value of k equals

    A
    `pi//12`
    B
    `pi//3`
    C
    `pi//2`
    D
    none of these

  • int_((pi)/(18))^((4pi)/(9))(2sqrt(sinx))/(sqrt(sinx)+sqrt(cosx))dx= . . .

    A
    `(7pi)/(36)`
    B
    `(5pi)/(36)`
    C
    `(7pi)/(18)`
    D
    `(5pi)/(18)`

  • int(sinx)/(sqrt(cos2x))dx=

    A
    `(-1)/(sqrt2)log[sqrt2 cos x+sqrt(cos2x)]+c`
    B
    `(-1)/(sqrt2)log[sqrt2 cos x+sqrt(2sin^(2)x-1)]+c`
    C
    `(-1)/(sqrt2)log[sqrt2 cos x+sqrt(1-2cos^(2)x)]+c`
    D
    `(-1)/(sqrt2)sec^(-1)(2cos^(2)x-1)+c`

    • Similar Questions

    Explore conceptually related problems

    Evalaute int_(pi//6)^(pi//3)(sqrt((sinx))dx)/(sqrt((sinx))+sqrt((cosx)))

    int_(0)^(pi//2)sqrt(1+sinx)dx

    int_(0)^(pi//2)(sqrt(cosx))/((sqrt(cosx)+sqrt(sinx)))dx=?

    I_(1) = int_(pi/6)^(pi/3) (dx)/(1+sqrt(tanx)) and I_(2) = (sqrt(sinx)dx)/(sqrt(sinx) + sqrt(cosx)) What is I_(1) - I_(2) equal to ?

    I_(1) = int_(pi/6)^(pi/3) (dx)/(1+sqrt(tanx)) and I_(2) = (sqrt(sinx)dx)/(sqrt(sinx) + sqrt(cosx)) What is I_(1) equal to ?

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