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"If "I=int sqrt((5-x)/(2+x))dx, " then "...

` "If "I=int sqrt((5-x)/(2+x))dx, " then " I " equals" `

A

`sqrt(x+2)sqrt(5-x)+3sin^(-1)sqrt((x+2)/(3))+C`

B

`sqrt(x+2)sqrt(5-x)+7sin^(-1)sqrt((x+2)/(7))+C`

C

`sqrt(x+2)sqrt(5-x)+5sin^(-1)sqrt((x+2)/(5))+C`

D

non of these

Text Solution

Verified by Experts

The correct Answer is:
B
`"Put " 2+x=t^(2), " so that "dx=2tdt. " Then " `
` I=int(sqrt(7-t^(2)))/(t)(2t)dt=2int sqrt(7-t^(2))dt`
`=tsqrt(7-t^(2))+7sin^(-1)((t)/(sqrt(7)))+C`
`=sqrt(x+2)sqrt(5-x)+7sin^(-1)((sqrt(x+2))/(sqrt(7)))+C`
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