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int(0)^(pi//2)(sinx)/((sinx+cosx))dx=?...

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

A

`pi`

B

`(pi)/(2)`

C

`0`

D

`(pi)/(4)`

Text Solution

AI Generated Solution

To solve the integral \( I = \int_{0}^{\frac{\pi}{2}} \frac{\sin x}{\sin x + \cos x} \, dx \), we can use the property of definite integrals. Here’s a step-by-step solution: ### Step 1: Define the Integral Let \[ I = \int_{0}^{\frac{\pi}{2}} \frac{\sin x}{\sin x + \cos x} \, dx \] ...
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int_(0)^(pi//2)(cosx)/((sinx+cosx))dx=(pi)/(4)

int_(0)^(pi//2)(x)/(sinx+cosx)dx .

Knowledge Check

  • int(sinx)/((sinx-cosx))dx=?

    A
    `(1)/(2)x-(1)/(2)log|sinx-cosx|+C`
    B
    `(1)/(2)x+(1)/(2)log|sinx-cosx|+C`
    C
    `log|sinx-cosx|+C`
    D
    none of these

  • Given int_(0)^(pi//2)(dx)/(1+sinx+cosx)=A . Then the value of the definite integral int_(0)^(pi//2)(sinx)/(1+sinx+cosx)dx is equal to

    A
    `1/2A`
    B
    `(pi)/2-A`
    C
    `(pi)/4-1/2A`
    D
    `(pi)/2+A`

  • int_(0)^(pi//2) (sin x) / ((sinx + cosx)^(2) ) dx =

    A
    `pi/2`
    B
    `pi/4`
    C
    `1/2`
    D
    `1/4`

    • Similar Questions

    Explore conceptually related problems

    Evaluate int_(0)^(pi//2)(x)/((sinx+cosx))dx .

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

    int_(0)^(pi//2) (sin x) / ((sinx + cosx)^(3) ) dx =

    int(sinx)/(sinx-cosx)dx=

    int_(0)^(pi//2)(sqrt(sinx)cosx)^(3)dx=?

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