यदि `int_(0)^(a) (1)/(4+x^(2))dx=pi/8, ` तब a का मान ज्ञात कीजिएः।

Explanation

`underset(0)overset(a)int (1)/(4+x^(2))dx=pi/8, `
`rArr underset(0)overset(a)int (1)/(x^(2)+2^(2))dx=pi/8`
`rArr [1/2tan^(-1)""pi/2]_(0)^(a)=pi/8`
`rArr 1/2tan^(-1)""a/2-1/2tan^(-1)0=pi/8`
`rArr 1/2tan^(-1)""a/2-0=pi/8`
`rArr tan^(-1)""a/2=pi/4`
`rArr a/2=tan(pi/4)=1`
`rArr a=2`