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int(0)^(pi//2) (cosx)/((4+sin x)(3+sin x...

`int_(0)^(pi//2) (cosx)/((4+sin x)(3+sin x) ) dx = `

A

`log (16/15)`

B

`log(15/16)`

C

`log (4/15)`

D

`log(15/4)`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • int_(0)^(pi//2) (cosx)/((1+sin x)(2+sin x) ) dx =

    A
    `log (2/3)`
    B
    `log(3/2)`
    C
    `log(4/3)`
    D
    `log(3/4)`

  • int_(0)^(pi//2)(cos x)/((3+sin x)(4+sin x))dx=

    A
    `log((4)/(3))`
    B
    `log((16)/(15))`
    C
    `log((15)/(16))`
    D
    `log((3)/(4))`

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

    A
    `(3pi)/10 - 1/10 log 3`
    B
    `(3pi)/10 + 1/10 log 3`
    C
    `(3pi)/20 - 1/10 log 3`
    D
    `(3pi)/20 + 1/10 log 3`

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

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

    int_(0)^(pi//2)(cosx)/((1+sin^(2)x))dx=?

    int_(0)^(pi//2) (cosx )/ (1+sin^(2)x)dx=

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