Question

If `int(sqrt(cotx))/(sinxcosx)dx=Psqrt(cotx)+Q,` then the value of P is
A. `-2`
B. 2
C. 3
D. `-3`

Answer 1

Correct Answer - 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`