int (0)^(1) (x)/(x^(2)+1)dx...

`int _(0)^(1) (x)/(x^(2)+1)dx`

Text Solution

Verified by Experts

`"Let "I= int_(0)^(1)(x)/(x^(2)+1)dx`
`"Let " x^(2)+1=t rArr xdx=(dt)/(2)`
`x=0 rArr t=1`
`" and " x=1 rArr t=2`
`:. I= int_(1)^(2) (1)/(t).(dt)/(2) =(1)/(2) int_(1)^(2) (1)/(t)dt =(1)/(2) [log |t|]_(1)^(2)`
`=(1)/(2)[log |2|-log |1|]=(1)/(2)log 2.`

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int_(0)^(1) x^(2)/(x^(2)+1)dx=

`2 - pi /4`

`2 + pi/4`

`1-pi/4`

`1+pi/4`

int_(0)^(1) (x^(2))/(1+x^(2))dx is equal to

`pi/4-1`

`1-pi/2`

`pi/2-1`

`1-pi/4`

The value of int_(0)^(1)(x^(2))/(1+x^(2))dx is

`1-(pi)/4`

`(pi)/4-1`

`1-(pi)/2`

`0`