Absolute value of sum of all integers in the domain of `f(x)=cot^(-1)sqrt((x+3)x)+cos^(-1)sqrt(x^2+3x+1)` is_______

Answer

`-3`

Explanation

We must have `x(x + 3) ge 0`
`rArr x ge 0 " or " x le -3`...(i)
Also, `-1 le x^(2) + 3x + 1 le 1`
`rArr x(x + 3) le 0 rArr -3 le x le 0`...(ii)
From Eqs. (i) and (ii), we get `x = {0, -3}`
Also, for these values `x^(2) + 3x + 1 ge -1`
Hence, the required sum is `-3`