`int_(0)^(9)(1)/(1+sqrtx)dx` का मान ज्ञात कीजिए ।

Explanation

माना `x=t^(2)`
`rArr" "dx=2t dt`
अब `{:(x=0," पर ",t=sqrt0=0),(x=9," पर ",t=sqrt9=3):}`
`therefore int_(0)^(9)(1)/(1+sqrtx)dx=int_(0)^(3)(2t dt)/(1+t)`
`" "=2int_(0)^(3)(1-(1)/(1+t))dt`
`" "=2[t-log|1+t|]_(0)^(3)`
`" "=2[(3-log4)-0]=2(3-log4)`