मूल्यांकन कीजिएः
`int_(0)^(3) (dx)/(9+x^(2))`

Explanation

`underset(0)overset(3)int (dx)/(9+x^(2))`
`underset(0)overset(3)int (dx)/(x^(2)+3^(2))`
`=[1/3tan^(-1)((x)/(3))]_(0)^(3) [therefore int(1)/(x^(2)+a^(2))dx=1/atan^(-1)((x)/(a))]`
`=1/3[tan^(-1)((3)/(3))-tan^(-1)(0)]`
`=1/3[tan^(-1)((3)/(3))-tan^(-1)(0)]`
`=1/3[tan^(-1)1-0]`
`=1/3(pi/4)=pi/12`