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If int(sqrt(cotx))/(sinxcosx)dx=Psqrt(co...

If `int(sqrt(cotx))/(sinxcosx)dx=Psqrt(cotx)+Q,` then the value of P is

A

`-2`

B

2

C

3

D

`-3`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `l=int(sqrt(cotx))/(sinx cosx)dx=int("cosec"^(2)x sqrt(cotx)dx)/(cotx)`
`" "["divide numerator and denominator by sin"^(2)x]`
`=int("cosec"^(2)x)/(sqrt(cotx))dx`
Put `cos x=t rArr -"cosec"^(2)x dx = dt`
`therefore" "l=int(-dt)/(sqrtt)=(-t^(1//2))/(1//2)+C=-2sqrt(cotx)+C`
`therefore" "P=-2`
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Knowledge Check

  • If int(sqrt(cotx))/(sinxcosx)dx=Psqrt(cotx)+Q , then P equals

    A
    1
    B
    2
    C
    `-1`
    D
    `-2`

  • If int(sqrt(cotx))/(sinx cos x)dx=a sqrt(cotx)+b , then

    A
    `a=1, b=-2`
    B
    `a=2, b=1`
    C
    `a=-1, b epsilon R`
    D
    `a=-2, b epsilon R`

  • int(cotx)/(1+sinx)dx=

    A
    `log((sinx)/(1-sinx))+c`
    B
    `log((sinx)/(1+sinx))+c`
    C
    `log((1+sinx)/(x))+c`
    D
    `log(1+sinx)+c`

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